Automorphism Classes of Quadilateral Actions on Sufaces of Genus 7 bdata: 7, 48, [ 2, 2, 2, 4 ] G = small group 38 of 52 group(s) of order 48 GrpPC : G of order 48 = 2^4 * 3 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.3^G.2 = G.3 * G.4, G.5^G.1 = G.5^2 12 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 48, [ 2, 2, 2, 4 ] G = small group 41 of 52 group(s) of order 48 GrpPC : G of order 48 = 2^4 * 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.3^G.1 = G.3 * G.4, G.3^G.2 = G.3 * G.4, G.5^G.1 = G.5^2 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 48, [ 2, 2, 2, 4 ] G = small group 48 of 52 group(s) of order 48 GrpPC : G of order 48 = 2^4 * 3 PC-Relations: G.1^2 = Id(G), 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 12 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 36, [ 2, 2, 2, 6 ] G = small group 10 of 14 group(s) of order 36 GrpPC : G of order 36 = 2^2 * 3^2 PC-Relations: G.1^2 = Id(G), G.2^2 = Id(G), G.3^3 = Id(G), G.4^3 = Id(G), G.3^G.2 = G.3^2, G.4^G.1 = G.4^2 12 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 32, [ 2, 2, 2, 8 ] G = small group 39 of 51 group(s) of order 32 GrpPC : G of order 32 = 2^5 PC-Relations: G.4^2 = G.5, G.2^G.1 = G.2 * G.4, G.4^G.1 = G.4 * G.5, G.4^G.2 = G.4 * G.5 3 generating vector(s) <, > <, > <, > bdata: 7, 32, [ 2, 2, 2, 8 ] G = small group 42 of 51 group(s) of order 32 GrpPC : G of order 32 = 2^5 PC-Relations: G.3^2 = G.5, G.4^2 = G.5, G.2^G.1 = G.2 * G.4, G.4^G.1 = G.4 * G.5, G.4^G.2 = G.4 * G.5 3 generating vector(s) <, > <, > <, > bdata: 7, 32, [ 2, 2, 2, 8 ] G = small group 43 of 51 group(s) of order 32 GrpPC : G of order 32 = 2^5 PC-Relations: G.4^2 = G.5, G.2^G.1 = G.2 * G.4, G.3^G.1 = G.3 * G.5, G.4^G.1 = G.4 * G.5, G.4^G.2 = G.4 * G.5 6 generating vector(s) <, > <, > <, > <, > <, > <, > bdata: 7, 28, [ 2, 2, 2, 14 ] G = small group 3 of 4 group(s) of order 28 GrpPC : G of order 28 = 2^2 * 7 PC-Relations: G.1^2 = Id(G), G.2^2 = Id(G), G.3^7 = Id(G), G.3^G.1 = G.3^6 3 generating vector(s) <, > <, > <, > bdata: 7, 24, [ 2, 2, 3, 6 ] G = small group 13 of 15 group(s) of order 24 GrpPC : G of order 24 = 2^3 * 3 PC-Relations: G.1^2 = Id(G), G.2^3 = Id(G), G.3^2 = Id(G), G.4^2 = Id(G), G.3^G.2 = G.4, G.4^G.2 = G.3 * G.4 8 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 24, [ 2, 2, 4, 4 ] G = small group 5 of 15 group(s) of order 24 GrpPC : G of order 24 = 2^3 * 3 PC-Relations: G.1^2 = Id(G), G.2^2 = G.3, G.3^2 = Id(G), G.4^3 = Id(G), G.4^G.1 = G.4^2 8 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 24, [ 2, 2, 4, 4 ] G = small group 8 of 15 group(s) of order 24 GrpPC : G of order 24 = 2^3 * 3 PC-Relations: G.1^2 = Id(G), G.2^2 = Id(G), G.3^2 = Id(G), G.4^3 = Id(G), G.2^G.1 = G.2 * G.3, G.4^G.1 = G.4^2 8 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 24, [ 2, 2, 4, 4 ] G = small group 12 of 15 group(s) of order 24 GrpPC : G of order 24 = 2^3 * 3 PC-Relations: G.1^2 = Id(G), G.2^3 = Id(G), G.3^2 = Id(G), G.4^2 = Id(G), G.2^G.1 = G.2^2, G.3^G.1 = G.4, G.3^G.2 = G.4, G.4^G.1 = G.3, G.4^G.2 = G.3 * G.4 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 18, [ 2, 2, 6, 6 ] G = small group 3 of 5 group(s) of order 18 GrpPC : G of order 18 = 2 * 3^2 PC-Relations: G.1^2 = Id(G), G.2^3 = Id(G), G.3^3 = Id(G), G.3^G.1 = G.3^2 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 16, [ 2, 2, 8, 8 ] G = small group 5 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.3, G.3^2 = G.4 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 16, [ 2, 2, 8, 8 ] G = small group 6 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.3, G.3^2 = G.4, G.2^G.1 = G.2 * G.4 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 16, [ 2, 2, 8, 8 ] G = small group 7 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.3^2 = G.4, G.2^G.1 = G.2 * G.3, G.3^G.1 = G.3 * G.4, G.3^G.2 = G.3 * G.4 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 16, [ 2, 2, 8, 8 ] G = small group 8 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.4, G.3^2 = G.4, G.2^G.1 = G.2 * G.3, G.3^G.1 = G.3 * G.4, G.3^G.2 = G.3 * G.4 4 generating vector(s) <, > <, > <, > <, > bdata: 7, 14, [ 2, 2, 14, 14 ] G = small group 2 of 2 group(s) of order 14 GrpPC : G of order 14 = 2 * 7 PC-Relations: G.1^2 = Id(G), G.2^7 = Id(G) 1 generating vector(s) <, > bdata: 7, 24, [ 2, 3, 3, 3 ] G = small group 3 of 15 group(s) of order 24 GrpPC : G of order 24 = 2^3 * 3 PC-Relations: G.1^3 = Id(G), G.2^2 = G.4, G.3^2 = G.4, G.4^2 = Id(G), G.2^G.1 = G.3, G.3^G.1 = G.2 * G.3, G.3^G.2 = G.3 * G.4 1 generating vector(s) <, > bdata: 7, 18, [ 2, 3, 3, 6 ] G = small group 3 of 5 group(s) of order 18 GrpPC : G of order 18 = 2 * 3^2 PC-Relations: G.1^2 = Id(G), G.2^3 = Id(G), G.3^3 = Id(G), G.3^G.1 = G.3^2 10 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 18, [ 2, 3, 3, 6 ] G = small group 5 of 5 group(s) of order 18 GrpPC : G of order 18 = 2 * 3^2 PC-Relations: G.1^2 = Id(G), G.2^3 = Id(G), G.3^3 = Id(G) 1 generating vector(s) <, > bdata: 7, 12, [ 2, 3, 12, 12 ] G = small group 2 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.3, G.2^3 = Id(G), G.3^2 = Id(G) 1 generating vector(s) <, > bdata: 7, 16, [ 2, 4, 4, 4 ] G = small group 2 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.3, G.2^2 = G.4 3 generating vector(s) <, > <, > <, > bdata: 7, 16, [ 2, 4, 4, 4 ] G = small group 4 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.4, G.2^2 = G.3, G.2^G.1 = G.2 * G.3 9 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 16, [ 2, 4, 4, 4 ] G = small group 12 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.1^2 = G.4, G.2^2 = G.4, G.2^G.1 = G.2 * G.4 1 generating vector(s) <, > bdata: 7, 16, [ 2, 4, 4, 4 ] G = small group 13 of 14 group(s) of order 16 GrpPC : G of order 16 = 2^4 PC-Relations: G.3^2 = G.4, G.2^G.1 = G.2 * G.4 3 generating vector(s) <, > <, > <, > bdata: 7, 12, [ 2, 4, 6, 12 ] G = small group 2 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.3, G.2^3 = Id(G), G.3^2 = Id(G) 1 generating vector(s) <, > bdata: 7, 12, [ 2, 6, 6, 6 ] G = small group 5 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = Id(G), G.2^2 = Id(G), G.3^3 = Id(G) 3 generating vector(s) <, > <, > <, > bdata: 7, 10, [ 2, 10, 10, 10 ] G = small group 2 of 2 group(s) of order 10 GrpPC : G of order 10 = 2 * 5 PC-Relations: G.1^2 = Id(G), G.2^5 = Id(G) 3 generating vector(s) <, > <, > <, > bdata: 7, 12, [ 3, 3, 4, 12 ] G = small group 2 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.3, G.2^3 = Id(G), G.3^2 = Id(G) 1 generating vector(s) <, > bdata: 7, 12, [ 3, 4, 4, 6 ] G = small group 1 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.2, G.2^2 = Id(G), G.3^3 = Id(G), G.3^G.1 = G.3^2 2 generating vector(s) <, > <, > bdata: 7, 12, [ 3, 4, 4, 6 ] G = small group 2 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.3, G.2^3 = Id(G), G.3^2 = Id(G) 1 generating vector(s) <, > bdata: 7, 9, [ 3, 9, 9, 9 ] G = small group 1 of 2 group(s) of order 9 GrpPC : G of order 9 = 3^2 PC-Relations: G.1^3 = G.2 6 generating vector(s) <, > <, > <, > <, > <, > <, > bdata: 7, 12, [ 4, 4, 4, 4 ] G = small group 1 of 5 group(s) of order 12 GrpPC : G of order 12 = 2^2 * 3 PC-Relations: G.1^2 = G.2, G.2^2 = Id(G), G.3^3 = Id(G), G.3^G.1 = G.3^2 16 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > bdata: 7, 8, [ 8, 8, 8, 8 ] G = small group 1 of 5 group(s) of order 8 GrpPC : G of order 8 = 2^3 PC-Relations: G.1^2 = G.2, G.2^2 = G.3 16 generating vector(s) <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, > <, >