g~:  33
r: 4


 b =  0 



Example  # 1
-- C~ --
G~ Id: SmallGroup <96, 82>
G~ name: (C4*C12):C2
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.4, 
    G.3^2 = G.5, 
    G.4^2 = Id(G), 
    G.5^2 = Id(G), 
    G.6^3 = Id(G), 
    G.2^G.1 = G.2 * G.5, 
    G.3^G.1 = G.3 * G.4, 
    G.6^G.1 = G.6^2
generating vector: [ G.1 * G.2 * G.3 * G.6, G.1 * G.4 * G.6^2, G.3 * G.4 * G.5, 
G.2 * G.5 * G.6^2 ]
signature: [ 2, 2, 4, 12 ]
genus: 33
decomp H^0(K_C~): [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 
1, 1, 0, 0, 1, 1, 2, 0, 1, 1 ]
N~ = dim S^2H^0(K_C~)^G~ = 10
sigma: G.4 * G.5
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 36>
G name: C2*D12
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = H.4, 
    H.3^2 = H.4, 
    H.4^2 = Id(H), 
    H.5^3 = Id(H), 
    H.2^H.1 = H.2 * H.4, 
    H.3^H.1 = H.3 * H.4, 
    H.5^H.1 = H.5^2
generating vector: [ H.1 * H.2 * H.3 * H.5, H.1 * H.4 * H.5^2, H.3, H.2 * H.4 * 
H.5^2 ]
signature: [ 2, 2, 4, 12 ]
genus: 17
decomp H^0(K_C): [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1 ]
N = dim S^2H^0(K_C)^G = 9

Example  # 2
-- C~ --
G~ Id: SmallGroup <96, 92>
G~ name: C2^2:C4:S3
GrpPC : G of order 96 = 2^5 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.4, 
    G.3^2 = Id(G), 
    G.4^2 = Id(G), 
    G.5^2 = Id(G), 
    G.6^3 = Id(G), 
    G.2^G.1 = G.2 * G.5, 
    G.3^G.1 = G.3 * G.4 * G.5, 
    G.3^G.2 = G.3 * G.5, 
    G.6^G.1 = G.6^2
generating vector: [ G.3 * G.5, G.1 * G.4 * G.6^2, G.1 * G.2 * G.3 * G.6, G.2 * 
G.6 ]
signature: [ 2, 2, 4, 12 ]
genus: 33
decomp H^0(K_C~): [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 
1, 1, 2, 2 ]
N~ = dim S^2H^0(K_C~)^G~ = 9
sigma: G.4 * G.5
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <48, 38>
G name: S3*D4
GrpPC : H of order 48 = 2^4 * 3
PC-Relations:
    H.1^2 = Id(H), 
    H.2^2 = H.4, 
    H.3^2 = Id(H), 
    H.4^2 = Id(H), 
    H.5^3 = Id(H), 
    H.2^H.1 = H.2 * H.4, 
    H.3^H.2 = H.3 * H.4, 
    H.5^H.1 = H.5^2
generating vector: [ H.3 * H.4, H.1 * H.4 * H.5^2, H.1 * H.2 * H.3 * H.5, H.2 * 
H.5 ]
signature: [ 2, 2, 4, 12 ]
genus: 17
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2 ]
N = dim S^2H^0(K_C)^G = 8

Example  # 3
-- C~ --
G~ Id: SmallGroup <96, 190>
G~ name: GL(2,3):C2
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.3^G.1 = G.3^2, 
    G.4^G.1 = G.5, 
    G.4^G.3 = G.5 * G.6, 
    G.5^G.1 = G.4, 
    G.5^G.3 = G.4 * G.5, 
    G.5^G.4 = G.5 * G.6
generating vector: [ G.1 * G.3^2 * G.4 * G.6, G.1 * G.3 * G.5, G.2 * G.3^2 * G.4
* G.5, G.2 * G.3^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 33
decomp H^0(K_C~): [ 0, 1, 0, 0, 1, 1, 1, 1, 2, 0, 2, 2, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 9
sigma: G.6
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 * H.5, H.2 * H.3^2 * H.4 * 
H.5, H.2 * H.3^2 ]
signature: [ 2, 2, 6, 6 ]
genus: 17
decomp H^0(K_C): [ 0, 0, 0, 1, 1, 1, 0, 2, 1, 1 ]
N = dim S^2H^0(K_C)^G = 8

Example  # 4
-- C~ --
G~ Id: SmallGroup <128, 525>
G~ name: C2^3.(C2*D4)
GrpPC : G of order 128 = 2^7
PC-Relations:
    G.1^2 = G.6, 
    G.3^2 = G.7, 
    G.4^2 = 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.7, 
    G.4^G.2 = G.4 * G.7, 
    G.4^G.3 = G.4 * G.7, 
    G.5^G.2 = G.5 * G.7
generating vector: [ G.2 * G.3 * G.5 * G.7, G.2 * G.4 * G.7, G.1 * G.6, G.1 * 
G.3 * G.4 * G.5 ]
signature: [ 2, 2, 4, 4 ]
genus: 33
decomp H^0(K_C~): [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 
1, 1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 9
sigma: G.7
branch points: 0
verify (B1): false
verify (B2): false
-- C --
G Id: SmallGroup <64, 60>
G name: C2^5.C2
GrpPC : H of order 64 = 2^6
PC-Relations:
    H.1^2 = H.6, 
    H.2^H.1 = H.2 * H.4, 
    H.3^H.1 = H.3 * H.5
generating vector: [ H.2 * H.3 * H.5, H.2 * H.4, H.1 * H.6, H.1 * H.3 * H.4 * 
H.5 ]
signature: [ 2, 2, 4, 4 ]
genus: 17
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
1, 0, 1, 1, 0, 1, 1, 0 ]
N = dim S^2H^0(K_C)^G = 8

Example  # 5
-- C~ --
G~ Id: SmallGroup <192, 1482>
G~ name: GL(2,3):C2:C2
GrpPC : G of order 192 = 2^6 * 3
PC-Relations:
    G.1^2 = Id(G), 
    G.2^2 = G.7, 
    G.3^2 = Id(G), 
    G.4^3 = Id(G), 
    G.5^2 = G.7, 
    G.6^2 = G.7, 
    G.7^2 = Id(G), 
    G.3^G.1 = G.3 * G.7, 
    G.4^G.1 = G.4^2, 
    G.5^G.1 = G.6, 
    G.5^G.4 = G.6 * G.7, 
    G.6^G.1 = G.5, 
    G.6^G.4 = G.5 * G.6, 
    G.6^G.5 = G.6 * G.7
generating vector: [ G.1 * G.7, G.1 * G.2 * G.3 * G.4, G.2 * G.6, G.3 * G.4^2 * 
G.5 ]
signature: [ 2, 2, 2, 6 ]
genus: 33
decomp H^0(K_C~): [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 
1, 1, 0, 1, 1, 0 ]
N~ = dim S^2H^0(K_C~)^G~ = 8
sigma: G.7
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.1 * H.2 * H.3 * H.4, H.2 * H.6, H.3 * H.4^2 * H.5 ]
signature: [ 2, 2, 2, 6 ]
genus: 17
decomp H^0(K_C): [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1 ]
N = dim S^2H^0(K_C)^G = 7
5