g~: 12 r: 4 b = 2 Example # 1 -- C~ -- G~ Id: SmallGroup <14, 2> G~ name: C14 GrpPC : G of order 14 = 2 * 7 PC-Relations: G.1^2 = Id(G), G.2^7 = Id(G) generating vector: [ G.2^3, G.2^2, G.1 * G.2, G.1 * G.2 ] signature: [ 7, 7, 14, 14 ] genus: 12 decomp H^0(K_C~): [ 0, 0, 0, 1, 1, 2, 1, 2, 1, 0, 1, 0, 2, 1 ] N~ = dim S^2H^0(K_C~)^G~ = 3 sigma: G.1 branch points: 2 verify (B1): true verify (B2): false -- C -- G Id: SmallGroup <7, 1> G name: C7 GrpPC : H of order 7 PC-Relations: H.1^7 = Id(H) generating vector: [ H.1^3, H.1^2, H.1, H.1 ] signature: [ 7, 7, 7, 7 ] genus: 6 decomp H^0(K_C): [ 0, 0, 1, 1, 1, 1, 2 ] N = dim S^2H^0(K_C)^G = 2 Example # 2 -- C~ -- G~ Id: SmallGroup <14, 2> G~ name: C14 GrpPC : G of order 14 = 2 * 7 PC-Relations: G.1^2 = Id(G), G.2^7 = Id(G) generating vector: [ G.2^5, G.2^4, G.1 * G.2^2, G.1 * G.2^3 ] signature: [ 7, 7, 14, 14 ] genus: 12 decomp H^0(K_C~): [ 0, 0, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0 ] N~ = dim S^2H^0(K_C~)^G~ = 4 sigma: G.1 branch points: 2 verify (B1): true verify (B2): false -- C -- G Id: SmallGroup <7, 1> G name: C7 GrpPC : H of order 7 PC-Relations: H.1^7 = Id(H) generating vector: [ H.1^5, H.1^4, H.1^2, H.1^3 ] signature: [ 7, 7, 7, 7 ] genus: 6 decomp H^0(K_C): [ 0, 1, 1, 1, 1, 1, 1 ] N = dim S^2H^0(K_C)^G = 3 Example # 3 -- C~ -- G~ Id: SmallGroup <20, 5> G~ name: C2*C10 GrpPC : G of order 20 = 2^2 * 5 PC-Relations: G.1^2 = Id(G), G.2^2 = Id(G), G.3^5 = Id(G) generating vector: [ G.1 * G.2, G.3^4, G.2 * G.3^4, G.1 * G.3^2 ] signature: [ 2, 5, 10, 10 ] genus: 12 decomp H^0(K_C~): [ 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0 ] N~ = dim S^2H^0(K_C~)^G~ = 3 sigma: G.1 branch points: 2 verify (B1): true verify (B2): false -- C -- G Id: SmallGroup <10, 2> G name: C10 GrpPC : H of order 10 = 2 * 5 PC-Relations: H.1^2 = Id(H), H.2^5 = Id(H) generating vector: [ H.1, H.2^4, H.1 * H.2^4, H.2^2 ] signature: [ 2, 5, 10, 5 ] genus: 6 decomp H^0(K_C): [ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1 ] N = dim S^2H^0(K_C)^G = 2 3