g~:  25
r: 4


 b =  0 



Example  # 1
-- C~ --
G~ Id: SmallGroup <48, 32>
G~ name: C2*SL(2,3)
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^3 = Id(G), 
    G.3^2 = G.5, 
    G.4^2 = G.5, 
    G.5^2 = Id(G), 
    G.3^G.2 = G.4, 
    G.4^G.2 = G.3 * G.4, 
    G.4^G.3 = G.4 * G.5
generating vector: [ G.1 * G.5, G.1 * G.2^2 * G.4 * G.5, G.1 * G.2^2, G.1 * 
G.2^2 * G.3 * G.4 * G.5 ]
signature: [ 2, 6, 6, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 1, 0, 0, 2, 2, 1, 2, 1, 0, 0, 3, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.5
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <24, 13>
G name: C2*A4
GrpPC : H of order 24 = 2^3 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^3 = Id(H), 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.3^H.2 = H.4, 
    H.4^H.2 = H.3 * H.4
generating vector: [ H.1, H.1 * H.2^2 * H.4, H.1 * H.2^2, H.1 * H.2^2 * H.3 * 
H.4 ]
signature: [ 2, 6, 6, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 1, 0, 2, 0, 1, 0, 3 ]
N = dim S^2H^0(K_C)^G = 7

Example  # 2
-- C~ --
G~ Id: SmallGroup <48, 30>
G~ name: A4:C4
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.4^2 = Id(G), 
    G.5^2 = Id(G), 
    G.3^G.1 = G.3^2, 
    G.4^G.1 = G.5, 
    G.4^G.3 = G.5, 
    G.5^G.1 = G.4, 
    G.5^G.3 = G.4 * G.5
generating vector: [ G.1 * G.5, G.1 * G.3^2 * G.4 * G.5, G.1 * G.3^2 * G.5, G.1 
* G.4 ]
signature: [ 4, 4, 4, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 2, 2, 0, 1, 3, 2, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 9
sigma: G.2
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <24, 12>
G name: S4
GrpPC : H of order 24 = 2^3 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^3 = Id(H), 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.2^H.1 = H.2^2, 
    H.3^H.1 = H.4, 
    H.3^H.2 = H.4, 
    H.4^H.1 = H.3, 
    H.4^H.2 = H.3 * H.4
generating vector: [ H.1 * H.4, H.1 * H.2^2 * H.3 * H.4, H.1 * H.2^2 * H.4, H.1 
* H.3 ]
signature: [ 4, 4, 4, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 1, 0, 1, 3 ]
N = dim S^2H^0(K_C)^G = 8

Example  # 3
-- C~ --
G~ Id: SmallGroup <56, 7>
G~ name: D14:C2
GrpPC : G of order 56 = 2^3 * 7
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = Id(G), 
    G.4^7 = Id(G), 
    G.2^G.1 = G.2 * G.3, 
    G.4^G.1 = G.4^6
generating vector: [ G.1 * G.4^6, G.1 * G.3 * G.4^2, G.2 * G.3 * G.4^6, G.2 * 
G.4^5 ]
signature: [ 2, 2, 14, 14 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 0, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.3
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <28, 3>
G name: D14
GrpPC : H of order 28 = 2^2 * 7
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^7 = Id(H), 
    H.3^H.1 = H.3^6
generating vector: [ H.1 * H.3^6, H.1 * H.3^2, H.2 * H.3^6, H.2 * H.3^5 ]
signature: [ 2, 2, 14, 14 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 7

Example  # 4
-- C~ --
G~ Id: SmallGroup <64, 6>
G~ name: D4:C8
GrpPC : G of order 64 = 2^6
PC-Relations:
    G.1^2 = G.4, 
    G.3^2 = G.5, 
    G.4^2 = G.6, 
    G.2^G.1 = G.2 * G.3, 
    G.3^G.1 = G.3 * G.5, 
    G.3^G.2 = G.3 * G.5
generating vector: [ G.2 * G.5 * G.6, G.2 * G.3 * G.5, G.1 * G.2 * G.4, G.1 * 
G.2 ]
signature: [ 2, 2, 8, 8 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 
1, 0, 1, 1, 1, 1, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.6
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <32, 9>
G name: D4:C4
GrpPC : H of order 32 = 2^5
PC-Relations:
    H.1^2 = H.4, 
    H.3^2 = H.5, 
    H.2^H.1 = H.2 * H.3, 
    H.3^H.1 = H.3 * H.5, 
    H.3^H.2 = H.3 * H.5
generating vector: [ H.2 * H.5, H.2 * H.3 * H.5, H.1 * H.2 * H.4, H.1 * H.2 ]
signature: [ 2, 2, 8, 8 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 5
-- C~ --
G~ Id: SmallGroup <64, 167>
G~ name: C4.SD16
GrpPC : G of order 64 = 2^6
PC-Relations:
    G.2^2 = G.5, 
    G.3^2 = G.4, 
    G.4^2 = G.6, 
    G.5^2 = G.6, 
    G.2^G.1 = G.2 * G.4, 
    G.3^G.1 = G.3 * G.5, 
    G.4^G.1 = G.4 * G.6, 
    G.5^G.1 = G.5 * G.6
generating vector: [ G.1 * G.2 * G.3 * G.5 * G.6, G.1 * G.5 * G.6, G.3 * G.4 * 
G.5 * G.6, G.2 * G.4 * G.5 * G.6 ]
signature: [ 2, 2, 8, 8 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 
1, 2 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.4 * G.5
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <32, 39>
G name: C2*D8
GrpPC : H of order 32 = 2^5
PC-Relations:
    H.2^2 = H.4, 
    H.3^2 = H.4 * H.5, 
    H.4^2 = H.5, 
    H.2^H.1 = H.2 * H.4 * H.5, 
    H.3^H.1 = H.3 * H.4, 
    H.4^H.1 = H.4 * H.5
generating vector: [ H.1 * H.2 * H.3 * H.4 * H.5, H.1 * H.4 * H.5, H.3 * H.5, 
H.2 * H.5 ]
signature: [ 2, 2, 8, 8 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 7

Example  # 6
-- C~ --
G~ Id: SmallGroup <64, 74>
G~ name: C2.(C4.D4)
GrpPC : G of order 64 = 2^6
PC-Relations:
    G.1^2 = G.4, 
    G.2^2 = G.4, 
    G.2^G.1 = G.2 * G.4, 
    G.3^G.1 = G.3 * G.5, 
    G.3^G.2 = G.3 * G.6
generating vector: [ G.3 * G.6, G.2 * G.3 * G.4 * G.6, G.1 * G.3 * G.4 * G.5, 
G.1 * G.2 * G.3 ]
signature: [ 2, 4, 4, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 
1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.4
branch points: 0
verify (B1): false
verify (B2): true
-- C --
G Id: SmallGroup <32, 27>
G name: C2^2wrC2
GrpPC : H of order 32 = 2^5
PC-Relations:
    H.3^H.1 = H.3 * H.4, 
    H.3^H.2 = H.3 * H.5
generating vector: [ H.3 * H.5, H.2 * H.3 * H.5, H.1 * H.3 * H.4, H.1 * H.2 * 
H.3 ]
signature: [ 2, 4, 4, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 7

Example  # 7
-- C~ --
G~ Id: SmallGroup <72, 22>
G~ name: D6:S3
GrpPC : G of order 72 = 2^3 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = Id(G), 
    G.4^3 = Id(G), 
    G.5^3 = Id(G), 
    G.2^G.1 = G.2 * G.3, 
    G.4^G.2 = G.4^2, 
    G.5^G.1 = G.5^2
generating vector: [ G.1, G.2 * G.4, G.1 * G.3 * G.4^2 * G.5, G.2 * G.5^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.3
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <36, 10>
G name: S3^2
GrpPC : H of order 36 = 2^2 * 3^2
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^3 = Id(H), 
    H.4^3 = Id(H), 
    H.3^H.2 = H.3^2, 
    H.4^H.1 = H.4^2
generating vector: [ H.1, H.2 * H.3, H.1 * H.3^2 * H.4, H.2 * H.4^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 1, 0, 1, 0, 1, 2 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 8
-- C~ --
G~ Id: SmallGroup <72, 30>
G~ name: C3*C3:D4
GrpPC : G of order 72 = 2^3 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.4^2 = Id(G), 
    G.5^3 = Id(G), 
    G.2^G.1 = G.2 * G.4, 
    G.5^G.1 = G.5^2
generating vector: [ G.1 * G.4 * G.5^2, G.1 * G.4 * G.5, G.2 * G.3^2 * G.4 * 
G.5^2, G.2 * G.3 * G.4 * G.5^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 
1, 1, 1, 1, 0, 0, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.4
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <36, 12>
G name: C6*S3
GrpPC : H of order 36 = 2^2 * 3^2
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^3 = Id(H), 
    H.4^3 = Id(H), 
    H.4^H.1 = H.4^2
generating vector: [ H.1 * H.4^2, H.1 * H.4, H.2 * H.3^2 * H.4^2, H.2 * H.3 * 
H.4^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 9
-- C~ --
G~ Id: SmallGroup <72, 35>
G~ name: C6^2:C2
GrpPC : G of order 72 = 2^3 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = Id(G), 
    G.4^3 = Id(G), 
    G.5^3 = Id(G), 
    G.2^G.1 = G.2 * G.3, 
    G.4^G.1 = G.4^2, 
    G.5^G.1 = G.5^2
generating vector: [ G.1 * G.3, G.1 * G.3 * G.4^2 * G.5^2, G.2 * G.3 * G.4^2, 
G.2 * G.3 * G.4^2 * G.5 ]
signature: [ 2, 2, 6, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 1, 
0 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.3
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <36, 13>
G name: C2*C3:S3
GrpPC : H of order 36 = 2^2 * 3^2
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^3 = Id(H), 
    H.4^3 = Id(H), 
    H.3^H.1 = H.3^2, 
    H.4^H.1 = H.4^2
generating vector: [ H.1, H.1 * H.3^2 * H.4^2, H.2 * H.3^2, H.2 * H.3^2 * H.4 ]
signature: [ 2, 2, 6, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 7

Example  # 10
-- C~ --
G~ Id: SmallGroup <96, 202>
G~ name: D4.A4
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.4^2 = G.6, 
    G.5^2 = G.6, 
    G.6^2 = Id(G), 
    G.2^G.1 = G.2 * G.6, 
    G.4^G.3 = G.5, 
    G.5^G.3 = G.4 * G.5, 
    G.5^G.4 = G.5 * G.6
generating vector: [ G.1 * G.2 * G.5, G.2, G.3 * G.5, G.1 * G.3^2 * G.4 * G.5 ]
signature: [ 2, 2, 3, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 6
sigma: G.6
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 49>
G name: C2^2*A4
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^3 = Id(H), 
    H.4^2 = Id(H), 
    H.5^2 = Id(H), 
    H.4^H.3 = H.5, 
    H.5^H.3 = H.4 * H.5
generating vector: [ H.1 * H.2 * H.5, H.2, H.3 * H.5, H.1 * H.3^2 * H.4 * H.5 ]
signature: [ 2, 2, 3, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1 ]
N = dim S^2H^0(K_C)^G = 5

Example  # 11
-- C~ --
G~ Id: SmallGroup <96, 32>
G~ name: (C3*OD16):C2
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.3, 
    G.3^2 = G.5, 
    G.4^2 = G.5, 
    G.5^2 = Id(G), 
    G.6^3 = Id(G), 
    G.2^G.1 = G.2 * G.4, 
    G.4^G.1 = G.4 * G.5, 
    G.4^G.2 = G.4 * G.5, 
    G.6^G.1 = G.6^2
generating vector: [ G.1 * G.5 * G.6^2, G.1, G.1 * G.2 * G.4 * G.6, G.1 * G.2 * 
G.3 ]
signature: [ 2, 2, 4, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 
0, 0, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 6
sigma: G.5
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 14>
G name: D6:C4
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = H.3, 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.5^3 = Id(H), 
    H.2^H.1 = H.2 * H.4, 
    H.5^H.1 = H.5^2
generating vector: [ H.1 * H.5^2, H.1, H.1 * H.2 * H.4 * H.5, H.1 * H.2 * H.3 ]
signature: [ 2, 2, 4, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0 ]
N = dim S^2H^0(K_C)^G = 5

Example  # 12
-- C~ --
G~ Id: SmallGroup <96, 186>
G~ name: C4*S4
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.3, 
    G.3^2 = Id(G), 
    G.4^3 = Id(G), 
    G.5^2 = Id(G), 
    G.6^2 = Id(G), 
    G.4^G.1 = G.4^2, 
    G.5^G.1 = G.6, 
    G.5^G.4 = G.6, 
    G.6^G.1 = G.5, 
    G.6^G.4 = G.5 * G.6
generating vector: [ G.1 * G.4^2 * G.5, G.1 * G.3 * G.4^2 * G.5, G.1 * G.2 * G.4
* G.5, G.1 * G.2 * G.4 * G.5 * G.6 ]
signature: [ 2, 2, 4, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.3
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 48>
G name: C2*S4
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^3 = Id(H), 
    H.4^2 = Id(H), 
    H.5^2 = Id(H), 
    H.3^H.1 = H.3^2, 
    H.4^H.1 = H.5, 
    H.4^H.3 = H.5, 
    H.5^H.1 = H.4, 
    H.5^H.3 = H.4 * H.5
generating vector: [ H.1 * H.3^2 * H.4, H.1 * H.3^2 * H.4, H.1 * H.2 * H.3 * 
H.4, H.1 * H.2 * H.3 * H.4 * H.5 ]
signature: [ 2, 2, 4, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 0, 0, 0, 1, 2, 0, 1 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 13
-- C~ --
G~ Id: SmallGroup <96, 203>
G~ name: C2^2:SL(2,3)
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^3 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = Id(G), 
    G.4^2 = G.6, 
    G.5^2 = G.6, 
    G.6^2 = Id(G), 
    G.2^G.1 = G.3, 
    G.3^G.1 = G.2 * G.3, 
    G.4^G.1 = G.5, 
    G.5^G.1 = G.4 * G.5, 
    G.5^G.4 = G.5 * G.6
generating vector: [ G.2 * G.3 * G.6, G.1 * G.2 * G.4 * G.5, G.1, G.1 * G.5 ]
signature: [ 2, 3, 3, 3 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 5
sigma: G.6
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 50>
G name: C2^4:C3
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^3 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.5^2 = Id(H), 
    H.2^H.1 = H.3, 
    H.3^H.1 = H.2 * H.3, 
    H.4^H.1 = H.5, 
    H.5^H.1 = H.4 * H.5
generating vector: [ H.2 * H.3, H.1 * H.2 * H.4 * H.5, H.1, H.1 * H.5 ]
signature: [ 2, 3, 3, 3 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 1, 1, 1, 0, 1, 1 ]
N = dim S^2H^0(K_C)^G = 4

Example  # 14
-- C~ --
G~ Id: SmallGroup <128, 357>
G~ name: C4^2.C2^3
GrpPC : G of order 128 = 2^7
PC-Relations:
    G.2^2 = G.7, 
    G.4^2 = G.6, 
    G.5^2 = G.7, 
    G.2^G.1 = G.2 * G.4, 
    G.3^G.1 = G.3 * G.5, 
    G.4^G.1 = G.4 * G.6, 
    G.4^G.2 = G.4 * G.6, 
    G.4^G.3 = G.4 * G.7, 
    G.5^G.1 = G.5 * G.7, 
    G.5^G.2 = G.5 * G.7, 
    G.5^G.3 = G.5 * G.7
generating vector: [ G.3 * G.5, G.2 * G.3 * G.4, G.1 * G.5 * G.6 * G.7, G.1 * 
G.2 * G.4 * G.6 ]
signature: [ 2, 2, 2, 8 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 
1, 0, 1, 1, 1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.7
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <64, 128>
G name: (C2*D8):C2
GrpPC : H of order 64 = 2^6
PC-Relations:
    H.4^2 = H.6, 
    H.2^H.1 = H.2 * H.4, 
    H.3^H.1 = H.3 * H.5, 
    H.4^H.1 = H.4 * H.6, 
    H.4^H.2 = H.4 * H.6
generating vector: [ H.3 * H.5, H.2 * H.3 * H.4, H.1 * H.5 * H.6, H.1 * H.2 * 
H.4 * H.6 ]
signature: [ 2, 2, 2, 8 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 15
-- C~ --
G~ Id: SmallGroup <144, 117>
G~ name: (C3*C6).D4
GrpPC : G of order 144 = 2^4 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = G.4, 
    G.4^2 = Id(G), 
    G.5^3 = Id(G), 
    G.6^3 = Id(G), 
    G.2^G.1 = G.2 * G.3, 
    G.3^G.1 = G.3 * G.4, 
    G.3^G.2 = G.3 * G.4, 
    G.5^G.1 = G.5^2, 
    G.5^G.2 = G.6, 
    G.5^G.3 = G.5^2, 
    G.6^G.2 = G.5, 
    G.6^G.3 = G.6^2
generating vector: [ G.1 * G.5, G.1 * G.4, G.2 * G.3 * G.4 * G.5 * G.6, G.2 * 
G.3 * G.5^2 * G.6 ]
signature: [ 2, 2, 2, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 6
sigma: G.4
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <72, 40>
G name: S3wrC2
GrpPC : H of order 72 = 2^3 * 3^2
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = Id(H), 
    H.4^3 = Id(H), 
    H.5^3 = Id(H), 
    H.2^H.1 = H.2 * H.3, 
    H.4^H.1 = H.4^2, 
    H.4^H.2 = H.5, 
    H.4^H.3 = H.4^2, 
    H.5^H.2 = H.4, 
    H.5^H.3 = H.5^2
generating vector: [ H.1 * H.4, H.1, H.2 * H.3 * H.4 * H.5, H.2 * H.3 * H.4^2 * 
H.5 ]
signature: [ 2, 2, 2, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 1, 0, 2, 1, 0, 0 ]
N = dim S^2H^0(K_C)^G = 5

Example  # 16
-- C~ --
G~ Id: SmallGroup <144, 153>
G~ name: S3*C3:D4
GrpPC : G of order 144 = 2^4 * 3^2
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = Id(G), 
    G.3^2 = Id(G), 
    G.4^2 = Id(G), 
    G.5^3 = Id(G), 
    G.6^3 = Id(G), 
    G.3^G.2 = G.3 * G.4, 
    G.5^G.2 = G.5^2, 
    G.6^G.1 = G.6^2
generating vector: [ G.1 * G.2 * G.4 * G.5^2 * G.6, G.2 * G.4, G.1 * G.3 * G.4, 
G.3 * G.4 * G.5^2 * G.6 ]
signature: [ 2, 2, 2, 6 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 
0, 1, 0, 1, 1, 0, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 7
sigma: G.4
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <72, 46>
G name: C2*S3^2
GrpPC : H of order 72 = 2^3 * 3^2
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = Id(H), 
    H.4^3 = Id(H), 
    H.5^3 = Id(H), 
    H.4^H.2 = H.4^2, 
    H.5^H.1 = H.5^2
generating vector: [ H.1 * H.2 * H.4^2 * H.5, H.2, H.1 * H.3, H.3 * H.4^2 * H.5 
]
signature: [ 2, 2, 2, 6 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0 ]
N = dim S^2H^0(K_C)^G = 6

Example  # 17
-- C~ --
G~ Id: SmallGroup <192, 312>
G~ name: C3:(C4wrC2:C2)
GrpPC : G of order 192 = 2^6 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.6, 
    G.3^2 = G.4 * G.6, 
    G.4^2 = G.6, 
    G.5^2 = Id(G), 
    G.6^2 = Id(G), 
    G.7^3 = Id(G), 
    G.3^G.1 = G.3 * G.4, 
    G.3^G.2 = G.3 * G.5, 
    G.4^G.1 = G.4 * G.6, 
    G.4^G.2 = G.4 * G.6, 
    G.5^G.1 = G.5 * G.6, 
    G.5^G.3 = G.5 * G.6, 
    G.7^G.1 = G.7^2
generating vector: [ G.1 * G.4 * G.6 * G.7^2, G.1 * G.3 * G.5 * G.7^2, G.1 * G.2
* G.4 * G.6 * G.7, G.1 * G.2 * G.3 * G.4 * G.5 * G.7 ]
signature: [ 2, 2, 2, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 
0, 0, 1, 1, 1, 0, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 6
sigma: G.6
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <96, 89>
G name: C2^2:D12
GrpPC : H of order 96 = 2^5 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = H.4, 
    H.4^2 = Id(H), 
    H.5^2 = Id(H), 
    H.6^3 = Id(H), 
    H.3^H.1 = H.3 * H.4, 
    H.3^H.2 = H.3 * H.5, 
    H.6^H.1 = H.6^2
generating vector: [ H.1 * H.4 * H.6^2, H.1 * H.3 * H.5 * H.6^2, H.1 * H.2 * H.4
* H.6, H.1 * H.2 * H.3 * H.4 * H.5 * H.6 ]
signature: [ 2, 2, 2, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 1 ]
N = dim S^2H^0(K_C)^G = 5

Example  # 18
-- C~ --
G~ Id: SmallGroup <192, 1478>
G~ name: Q8:S4
GrpPC : G of order 192 = 2^6 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.4, 
    G.3^2 = G.4, 
    G.4^2 = Id(G), 
    G.5^3 = Id(G), 
    G.6^2 = Id(G), 
    G.7^2 = Id(G), 
    G.3^G.1 = G.3 * G.4, 
    G.3^G.2 = G.3 * G.4, 
    G.5^G.1 = G.5^2, 
    G.6^G.1 = G.7, 
    G.6^G.5 = G.7, 
    G.7^G.1 = G.6, 
    G.7^G.5 = G.6 * G.7
generating vector: [ G.1 * G.3 * G.5^2 * G.6, G.1 * G.4 * G.5 * G.7, G.1 * G.2 *
G.3 * G.5^2, G.1 * G.2 * G.7 ]
signature: [ 2, 2, 2, 4 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 
0, 1, 1, 1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 6
sigma: G.4
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <96, 226>
G name: C2^2*S4
GrpPC : H of order 96 = 2^5 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = Id(H), 
    H.3^2 = Id(H), 
    H.4^3 = Id(H), 
    H.5^2 = Id(H), 
    H.6^2 = Id(H), 
    H.4^H.1 = H.4^2, 
    H.5^H.1 = H.6, 
    H.5^H.4 = H.6, 
    H.6^H.1 = H.5, 
    H.6^H.4 = H.5 * H.6
generating vector: [ H.1 * H.3 * H.4^2 * H.5, H.1 * H.4 * H.6, H.1 * H.2 * H.3 *
H.4^2, H.1 * H.2 * H.6 ]
signature: [ 2, 2, 2, 4 ]
genus: 13
decomp H^0(K_C): [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 5
18


 b =  16 



Example  # 1
-- C~ --
G~ Id: SmallGroup <128, 749>
G~ name: C4.C2^2wrC2
GrpPC : G of order 128 = 2^7
PC-Relations:
    G.4^2 = G.7, 
    G.5^2 = G.7, 
    G.6^2 = G.7, 
    G.2^G.1 = G.2 * G.4, 
    G.3^G.1 = G.3 * G.5, 
    G.3^G.2 = G.3 * G.6, 
    G.4^G.1 = G.4 * G.7, 
    G.4^G.2 = G.4 * G.7, 
    G.5^G.1 = G.5 * G.7, 
    G.5^G.3 = G.5 * G.7, 
    G.6^G.2 = G.6 * G.7, 
    G.6^G.3 = G.6 * G.7
generating vector: [ G.2 * G.6 * G.7, G.3 * G.5 * G.6 * G.7, G.1 * G.4, G.1 * 
G.2 * G.3 * G.4 * G.5 * G.6 * G.7 ]
signature: [ 2, 2, 2, 8 ]
genus: 25
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 
0, 1, 2, 0, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 5
sigma: G.7
branch points: 16
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <64, 73>
G name: C2.C4:D4
GrpPC : H of order 64 = 2^6
PC-Relations:
    H.2^H.1 = H.2 * H.4, 
    H.3^H.1 = H.3 * H.5, 
    H.3^H.2 = H.3 * H.6
generating vector: [ H.2 * H.6, H.3 * H.5 * H.6, H.1 * H.4, H.1 * H.2 * H.3 * 
H.4 * H.5 * H.6 ]
signature: [ 2, 2, 2, 4 ]
genus: 9
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 
1, 0 ]
N = dim S^2H^0(K_C)^G = 4
1