|
{
"version": "01-May-2025, 05:40:21 UTC",
"idenum": "CTblLib.Data.IdEnumerator",
"attrid": "prim",
"automatic": [
["(7^2)b:2.L2(7).2",["hard test",[[49,31]]]],
["(A4wr2^2):2",["hard test",[[256,13]]]],
["(A5xA5):2",["hard test",[[60,2]]]],
["(A5xA5):2^2",["hard test",[[25,24],[36,18],[60,5],[100,6]]]],
["(A5xA5):4",["hard test",[[25,25],[36,19],[100,7]]]],
["(A6xA6).D8",["hard test",[[100,27],[1296,11],[2025,11]]]],
["(A6xA6):2^2",["hard test",[[36,14],[100,19],[225,3],[360,11],[360,14]]]],
["(D10xD10).2^2",["prim. group on solv. minimal normal subgroup (classes test)",[[25,11]]]],
["(L2(11)xL2(11)):4",["hard test",[[144,14],[3025,2],[3025,4]]]],
["(L3(2)xL3(2)).4",["hard test",[[64,71],[441,23],[784,2]]]],
["(L3(2)xL3(2)):2",["hard test",[[168,2]]]],
["(S5xS5xS5):S3",["hard test",[[125,35],[216,20],[1000,10]]]],
["(S6wr2).2",["hard test",[[100,34],[1296,22],[2025,19]]]],
["(S6xS6).2^2",["hard test",[[100,34],[1296,22],[2025,19]]]],
["(S6xS6).4",["hard test",[[100,35],[1296,17],[2025,18]]]],
["(S6xS6):2",["hard test",[[36,16],[100,22],[225,5]]]],
["109:54",["prim. group on solv. minimal normal subgroup",[[109,11]]]],
["113:56",["prim. group on solv. minimal normal subgroup",[[113,9]]]],
["11:10",["prim. group on solv. minimal normal subgroup",[[11,4]]]],
["11:5",["prim. group on solv. minimal normal subgroup",[[11,3]]]],
["11^2:(5x2.A5)",["prim. group on solv. minimal normal subgroup",[[121,57]]]],
["11^2:(5x2L2(11).2)",["hard test",[[121,46]]]],
["11^2:60",["prim. group on solv. minimal normal subgroup (classes test)",[[121,32]]]],
["127:7",["prim. group on solv. minimal normal subgroup",[[127,5]]]],
["13:12",["prim. group on solv. minimal normal subgroup",[[13,6]]]],
["13:3",["prim. group on solv. minimal normal subgroup",[[13,3]]]],
["13:4",["prim. group on solv. minimal normal subgroup",[[13,4]]]],
["13:6",["prim. group on solv. minimal normal subgroup",[[13,5]]]],
["13^2:2.L2(13).4",["hard test",[[169,64]]]],
["17:16",["prim. group on solv. minimal normal subgroup",[[17,5]]]],
["17:8",["prim. group on solv. minimal normal subgroup",[[17,4]]]],
["19:18",["prim. group on solv. minimal normal subgroup",[[19,6]]]],
["19:3",["prim. group on solv. minimal normal subgroup",[[19,3]]]],
["19:6",["prim. group on solv. minimal normal subgroup",[[19,4]]]],
["19:9",["prim. group on solv. minimal normal subgroup",[[19,5]]]],
["23:11",["prim. group on solv. minimal normal subgroup",[[23,3]]]],
["23:22",["prim. group on solv. minimal normal subgroup",[[23,4]]]],
["29:14",["prim. group on solv. minimal normal subgroup",[[29,5]]]],
["2E6(2)M8",["simple group",[[3510,1]]]],
["2E6(2)M9",["simple group",[[3510,1]]]],
["2F4(2)'",["simple group",[[1600,20],[1755,1],[2304,9],[2925,1]]]],
["2F4(2)'.2",["unique almost simple group with the given socle and socle factor",[[1755,2],[2304,10],[2925,2]]]],
["2F4(2)'M2",["unique almost simple group with the given socle and socle factor",[[52,1],[117,1],[144,2],[234,2]]]],
["2F4(2)'M7",["unique almost simple group with the given socle and socle factor",[[10,7],[36,5],[45,3]]]],
["2^10:L5(2)",["prim. group on solv. minimal normal subgroup",[[1024,83]]]],
["2^10:M22'",["prim. group on solv. minimal normal subgroup (classes test)",[[1024,74]]]],
["2^10:m22",["prim. group on solv. minimal normal subgroup (classes test)",[[1024,73]]]],
["2^10:m22:2",["prim. group on solv. minimal normal subgroup (classes test)",[[1024,79]]]],
["2^11:M24",["prim. group on solv. minimal normal subgroup (classes test)",[[2048,10]]]],
["2^3.7.3",["prim. group on solv. minimal normal subgroup",[[8,2]]]],
["2^3:7",["prim. group on solv. minimal normal subgroup",[[8,1]]]],
["2^3:sl(3,2)",["prim. group on solv. minimal normal subgroup",[[8,3]]]],
["2^4:(3xA5).2",["hard test",[[16,12]]]],
["2^4:(S3xS3)",["hard test",[[16,7]]]],
["2^4:3^2:4",["hard test",[[16,8]]]],
["2^4:A5",["prim. group on solv. minimal normal subgroup (classes test)",[[16,15]]]],
["2^4:a6",["unique perfect group of its order",[[16,17]]]],
["2^4:a7",["prim. group on solv. minimal normal subgroup",[[16,20]]]],
["2^4:a8",["prim. group on solv. minimal normal subgroup",[[16,11]]]],
["2^4:s5",["prim. group on solv. minimal normal subgroup (classes test)",[[16,13]]]],
["2^5:L5(2)",["prim. group on solv. minimal normal subgroup",[[32,3]]]],
["2^6:(7xL2(8))",["hard test",[[64,51]]]],
["2^6:(psl(3,2)xs3)",["hard test",[[64,53]]]],
["2^6:3.s6",["prim. group on solv. minimal normal subgroup",[[64,47]]]],
["2^6:3^(1+2).D8",["prim. group on solv. minimal normal subgroup (classes test)",[[64,27]]]],
["2^6:3^3:S4",["hard test",[[64,36]]]],
["2^6:A7",["prim. group on solv. minimal normal subgroup",[[64,61]]]],
["2^6:A8",["prim. group on solv. minimal normal subgroup",[[64,59]]]],
["2^6:L6(2)",["prim. group on solv. minimal normal subgroup",[[64,41]]]],
["2^6:S7",["hard test",[[64,60]]]],
["2^6:S8",["prim. group on solv. minimal normal subgroup",[[64,58]]]],
["2^6:U4(2)",["prim. group on solv. minimal normal subgroup",[[64,57]]]],
["2^6:U4(2).2",["prim. group on solv. minimal normal subgroup",[[64,56]]]],
["2^6:s6f2",["prim. group on solv. minimal normal subgroup",[[64,55]]]],
["2^6:u3(3)",["prim. group on solv. minimal normal subgroup",[[64,63]]]],
["2^8.A9",["prim. group on solv. minimal normal subgroup (classes test)",[[256,218]]]],
["2^8:O8+(2)",["prim. group on solv. minimal normal subgroup",[[256,234]]]],
["2^8:O8+(2):2",["prim. group on solv. minimal normal subgroup",[[256,236]]]],
["2^8:O8-(2)",["prim. group on solv. minimal normal subgroup",[[256,235]]]],
["2^8:O8-(2):2",["prim. group on solv. minimal normal subgroup",[[256,237]]]],
["2^8:S6(2)",["prim. group on solv. minimal normal subgroup",[[256,227]]]],
["2^8:S8",["prim. group on solv. minimal normal subgroup",[[256,200]]]],
["2^8:S8(2)",["prim. group on solv. minimal normal subgroup",[[256,243]]]],
["2^9.L3(4)",["prim. group on solv. minimal normal subgroup",[[512,46]]]],
["31:10",["prim. group on solv. minimal normal subgroup",[[31,6]]]],
["31:15",["prim. group on solv. minimal normal subgroup",[[31,7]]]],
["31:3",["prim. group on solv. minimal normal subgroup",[[31,3]]]],
["31:30",["prim. group on solv. minimal normal subgroup",[[31,8]]]],
["31:5",["prim. group on solv. minimal normal subgroup",[[31,4]]]],
["31:6",["prim. group on solv. minimal normal subgroup",[[31,5]]]],
["37:12",["prim. group on solv. minimal normal subgroup",[[37,7]]]],
["37:18",["prim. group on solv. minimal normal subgroup",[[37,8]]]],
["37:3",["prim. group on solv. minimal normal subgroup",[[37,3]]]],
["3D4(2)",["simple group",[[819,5],[2457,1]]]],
["3D4(2).3",["unique almost simple group with the given socle and socle factor",[[819,6],[2457,2]]]],
["3^2.2.S4",["hard test",[[9,7]]]],
["3^2:2A4",["hard test",[[9,6]]]],
["3^2:4",["prim. group on solv. minimal normal subgroup",[[9,1]]]],
["3^2:Q8",["prim. group on solv. minimal normal subgroup (classes test)",[[9,3]]]],
["3^2:Q8.2",["prim. group on solv. minimal normal subgroup",[[9,5]]]],
["3^3.S4",["hard test",[[27,3]]]],
["3^3:13",["prim. group on solv. minimal normal subgroup",[[27,2]]]],
["3^3:A4",["hard test",[[27,1]]]],
["3^3:L3(3)",["unique perfect group of its order",[[27,10]]]],
["3^3:S4`",["hard test",[[27,5]]]],
["3^4.2U4(2)",["prim. group on solv. minimal normal subgroup",[[81,132]]]],
["3^4.2U4(2).2",["prim. group on solv. minimal normal subgroup",[[81,131]]]],
["3^4.A6.D8",["hard test",[[81,140]]]],
["3^4:(2xA5)",["hard test",[[81,144]]]],
["3^4:(2xA6)",["prim. group on solv. minimal normal subgroup (classes test)",[[81,134]]]],
["3^4:(M10x2)",["hard test",[[81,139]]]],
["3^4:2(A4xA4).2",["hard test",[[81,96]]]],
["3^4:2(A4xA4).4",["hard test",[[81,104]]]],
["3^4:2(S4xS4).2",["hard test",[[81,107]]]],
["3^4:2^(1+4).(5:4)",["prim. group on solv. minimal normal subgroup",[[81,99]]]],
["3^4:2^(1+4)D10",["prim. group on solv. minimal normal subgroup (classes test)",[[81,90]]]],
["3^4:2^3.S4",["hard test",[[81,73]]]],
["3^4:2^3.S4(a)",["hard test",[[81,74]]]],
["3^4:40",["prim. group on solv. minimal normal subgroup (classes test)",[[81,25]]]],
["3^4:A6",["prim. group on solv. minimal normal subgroup",[[81,133]]]],
["3^4:GL2(9)",["hard test",[[81,118]]]],
["3^4:S5",["prim. group on solv. minimal normal subgroup (classes test)",[[81,142]]]],
["3^4:S6",["hard test",[[81,135]]]],
["3^4:m10",["prim. group on solv. minimal normal subgroup (classes test)",[[81,136]]]],
["3^5:(2xU4(2).2)",["hard test",[[243,28]]]],
["3^5:(2xm11)",["hard test",[[243,31]]]],
["3^5:(M11x2)",["hard test",[[243,29]]]],
["3^5:M11",["prim. group on solv. minimal normal subgroup (classes test)",[[243,30]]]],
["3^5:U4(2)",["prim. group on solv. minimal normal subgroup",[[243,24]]]],
["3^5:U4(2):2",["prim. group on solv. minimal normal subgroup (classes test)",[[243,27]]]],
["3^6:(L4(3)x2)",["prim. group on solv. minimal normal subgroup (classes test)",[[729,471]]]],
["3^6:2M12",["prim. group on solv. minimal normal subgroup",[[729,462]]]],
["3^6:2U4(3).2_1",["prim. group on solv. minimal normal subgroup (classes test)",[[729,474]]]],
["3^6:L3(3)",["prim. group on solv. minimal normal subgroup",[[729,416]]]],
["3^6:L4(3)",["prim. group on solv. minimal normal subgroup",[[729,468]]]],
["3^7:O7(3)",["prim. group on solv. minimal normal subgroup",[[2187,65]]]],
["41:4",["prim. group on solv. minimal normal subgroup",[[41,3]]]],
["41:40",["prim. group on solv. minimal normal subgroup",[[41,8]]]],
["43:14",["prim. group on solv. minimal normal subgroup",[[43,6]]]],
["43:3",["prim. group on solv. minimal normal subgroup",[[43,3]]]],
["47:23",["prim. group on solv. minimal normal subgroup",[[47,3]]]],
["59:29",["prim. group on solv. minimal normal subgroup",[[59,3]]]],
["5:4",["prim. group on solv. minimal normal subgroup",[[5,3]]]],
["5^2:(4xS3)",["prim. group on solv. minimal normal subgroup (classes test)",[[25,13]]]],
["5^2:12",["hard test",[[25,9]]]],
["5^2:2A5",["unique perfect group of its order",[[25,20]]]],
["5^2:4A4",["prim. group on solv. minimal normal subgroup (classes test)",[[25,18]]]],
["5^2:4s5",["hard test",[[25,22]]]],
["5^2:D12",["hard test",[[25,7]]]],
["5^2:S3",["prim. group on solv. minimal normal subgroup (classes test)",[[25,2]]]],
["5^3:(2xA5).2",["hard test",[[125,44]]]],
["5^3:(4xS5)",["hard test",[[125,45]]]],
["5^3:62",["prim. group on solv. minimal normal subgroup",[[125,10]]]],
["67:22",["prim. group on solv. minimal normal subgroup",[[67,6]]]],
["73:3",["prim. group on solv. minimal normal subgroup",[[73,3]]]],
["7:3",["prim. group on solv. minimal normal subgroup",[[7,3]]]],
["7:6",["prim. group on solv. minimal normal subgroup",[[7,4]]]],
["7^2:(3x2A4)",["prim. group on solv. minimal normal subgroup (classes test)",[[49,27]]]],
["7^2:(3x2S4)",["prim. group on solv. minimal normal subgroup",[[49,29]]]],
["7^2:2.L2(7).2",["hard test",[[49,31]]]],
["7^2:24",["prim. group on solv. minimal normal subgroup (classes test)",[[49,15]]]],
["7^2:2A4",["hard test",[[49,17]]]],
["7^2:2psl(2,7)",["unique perfect group of its order",[[49,30]]]],
["7^2:S3",["prim. group on solv. minimal normal subgroup",[[49,2]]]],
["A10",["simple group",[[10,8],[45,6],[120,18],[126,1],[210,1],[945,1],[2520,6]]]],
["A10.2",["unique almost simple group with the given socle and socle factor",[[10,9],[45,7],[120,19],[126,2],[210,2],[945,2],[2520,7]]]],
["A11",["simple group",[[11,7],[55,5],[165,4],[330,3],[462,3],[2520,8]]]],
["A11.2",["unique almost simple group with the given socle and socle factor",[[11,8],[55,6],[165,5],[330,4],[462,4]]]],
["A12",["simple group",[[12,5],[66,4],[220,2],[462,1],[495,7],[792,1],[2520,9]]]],
["A12.2",["unique almost simple group with the given socle and socle factor",[[12,6],[66,5],[220,3],[462,2],[495,8],[792,2]]]],
["A13",["simple group",[[13,8],[78,3],[286,1],[715,1],[1287,1],[1716,1]]]],
["A13.2",["unique almost simple group with the given socle and socle factor",[[13,9],[78,4],[286,2],[715,2],[1287,2],[1716,2]]]],
["A14",["simple group",[[14,3],[91,5],[364,6],[1001,1],[1716,3],[2002,1],[3003,1]]]],
["A14.2",["unique almost simple group with the given socle and socle factor",[[14,4],[91,6],[364,7],[1001,2],[1716,4],[2002,2],[3003,2]]]],
["A15",["simple group",[[15,5],[105,8],[455,1],[1365,5],[3003,3]]]],
["A15.2",["unique almost simple group with the given socle and socle factor",[[15,6],[105,9],[455,2],[1365,6],[3003,4]]]],
["A16",["simple group",[[16,21],[120,20],[560,3],[1820,1]]]],
["A16.2",["unique almost simple group with the given socle and socle factor",[[16,22],[120,21],[560,4],[1820,2]]]],
["A17",["simple group",[[17,9],[136,11],[680,1],[2380,5]]]],
["A17.2",["unique almost simple group with the given socle and socle factor",[[17,10],[136,12],[680,2],[2380,6]]]],
["A18",["simple group",[[18,3],[153,3],[816,1],[3060,1]]]],
["A18.2",["unique almost simple group with the given socle and socle factor",[[18,4],[153,4],[816,2],[3060,2]]]],
["A19",["simple group",[[19,7],[171,3],[969,1],[3876,1]]]],
["A19.2",["unique almost simple group with the given socle and socle factor",[[19,8],[171,4],[969,2],[3876,2]]]],
["A5",["simple group",[[5,4],[6,1],[10,1]]]],
["A5.2",["unique almost simple group with the given socle and socle factor",[[5,5],[6,2],[10,2]]]],
["A5xA5",["unique perfect group of its order",[[60,1]]]],
["A6",["simple group",[[6,3],[10,3],[15,2]]]],
["A6.2^2",["unique almost simple group with the given socle and socle factor",[[10,7],[36,5],[45,3]]]],
["A6.2_1",["almost simple group with the given socle and socle factor that fits",[[6,4],[10,5],[15,3]]]],
["A6.2_1M3",["unique almost simple group with the given socle and socle factor",[[5,5],[6,2],[10,2]]]],
["A6.2_2",["almost simple group with the given socle and socle factor that fits",[[10,4],[36,4],[45,1]]]],
["A6.2_3",["almost simple group with the given socle and socle factor that fits",[[10,6],[36,3],[45,2]]]],
["A6M2",["simple group",[[5,4],[6,1],[10,1]]]],
["A6M5",["hard test",[[4,2]]]],
["A7",["simple group",[[7,6],[15,1],[21,2],[35,3]]]],
["A7.2",["unique almost simple group with the given socle and socle factor",[[7,7],[21,3],[35,4],[120,1]]]],
["A8",["simple group",[[8,6],[15,4],[28,7],[35,1],[56,6]]]],
["A8.2",["unique almost simple group with the given socle and socle factor",[[8,7],[28,8],[35,2],[56,7],[105,7],[120,11]]]],
["A9",["simple group",[[9,10],[36,11],[84,1],[120,2],[126,12],[280,1],[840,1]]]],
["A9.2",["unique almost simple group with the given socle and socle factor",[[9,11],[36,12],[84,2],[126,13],[280,2],[840,2]]]],
["A9M5",["unique almost simple group with the given socle and socle factor",[[9,9],[28,3],[36,2]]]],
["Co2",["simple group",[[2300,1]]]],
["Co3",["simple group",[[276,3]]]],
["D10",["prim. group on solv. minimal normal subgroup",[[5,2]]]],
["D122",["prim. group on solv. minimal normal subgroup",[[61,2]]]],
["D14",["prim. group on solv. minimal normal subgroup",[[7,2]]]],
["D22",["prim. group on solv. minimal normal subgroup",[[11,2]]]],
["D26",["prim. group on solv. minimal normal subgroup",[[13,2]]]],
["D62",["prim. group on solv. minimal normal subgroup",[[31,2]]]],
["F3+M14",["unique almost simple group with the given socle and socle factor",[[2058,2]]]],
["F4(2)M10",["unique almost simple group with the given socle and socle factor",[[819,6],[2457,2]]]],
["F4(2)M4",["simple group",[[120,15],[136,6],[255,1],[2295,1]]]],
["F4(2)M8",["unique almost simple group with the given socle and socle factor",[[1575,4]]]],
["Fi22",["simple group",[[3510,1]]]],
["Fi22.2",["unique almost simple group with the given socle and socle factor",[[3510,2]]]],
["Fi22.2M4",["prim. group on solv. minimal normal subgroup (classes test)",[[1024,78]]]],
["Fi22M3",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["Fi22N5",["prim. group on solv. minimal normal subgroup",[[25,19]]]],
["G2(3)",["simple group",[[351,7],[364,5],[378,7],[2808,1],[3159,1],[3888,1]]]],
["G2(3).2",["unique almost simple group with the given socle and socle factor",[[1456,3],[2808,2],[3159,2],[3888,2]]]],
["G2(3)M2",["unique almost simple group with the given socle and socle factor",[[28,5],[36,7],[63,2],[63,4]]]],
["G2(3)M6",["unique almost simple group with the given socle and socle factor",[[52,1],[117,1],[144,2],[234,2]]]],
["G2(4)",["simple group",[[416,7],[1365,1],[1365,2],[2016,7],[2080,7]]]],
["G2(4).2",["unique almost simple group with the given socle and socle factor",[[416,4],[1365,3],[1365,4],[2016,8],[2080,8]]]],
["G2(5)",["simple group",[[3906,1],[3906,2]]]],
["HNM12",["unique almost simple group with the given socle and socle factor",[[144,4],[144,5],[396,2],[495,4],[495,6],[880,1],[1320,2],[1584,1]]]],
["HS",["simple group",[[100,3],[176,4],[1100,1],[1100,2],[3850,1]]]],
["HS.2",["unique almost simple group with the given socle and socle factor",[[100,4],[1100,3],[1100,4],[3850,2]]]],
["HSM3",["unique almost simple group with the given socle and socle factor",[[50,2],[126,4],[175,4],[525,2],[750,1]]]],
["HSM9",["simple group",[[11,6],[12,1],[55,4],[66,2],[165,3]]]],
["He",["simple group",[[2058,1]]]],
["He.2",["unique almost simple group with the given socle and socle factor",[[2058,2]]]],
["J1",["simple group",[[266,1],[1045,1],[1463,1],[1540,1],[1596,1],[2926,1]]]],
["J2",["simple group",[[100,1],[280,21],[315,2],[525,5],[840,3],[1008,1],[1800,1],[2016,3]]]],
["J2.2",["unique almost simple group with the given socle and socle factor",[[100,2],[280,22],[315,3],[525,6],[840,4],[1008,2],[1800,2],[2016,5]]]],
["J3M3",["simple group",[[20,1],[57,1],[171,1],[190,1]]]],
["L2(101)",["simple group",[[102,2]]]],
["L2(103)",["simple group",[[104,1]]]],
["L2(107)",["simple group",[[108,1]]]],
["L2(109)",["simple group",[[110,1]]]],
["L2(11)",["simple group",[[11,5],[12,3],[55,1]]]],
["L2(11).2",["unique almost simple group with the given socle and socle factor",[[12,4],[55,2],[55,3],[66,1]]]],
["L2(113)",["simple group",[[114,1]]]],
["L2(121)",["simple group",[[122,1],[671,1]]]],
["L2(121)M3",["unique almost simple group with the given socle and socle factor",[[12,4],[55,2],[55,3],[66,1]]]],
["L2(125)",["simple group",[[126,14]]]],
["L2(13)",["simple group",[[14,1],[78,1],[91,1],[91,3]]]],
["L2(13).2",["unique almost simple group with the given socle and socle factor",[[14,2],[78,2],[91,2],[91,4]]]],
["L2(16)",["simple group",[[17,6],[68,1],[120,3],[136,3]]]],
["L2(16).2",["unique almost simple group with the given socle and socle factor",[[17,7],[68,2],[120,4],[136,4]]]],
["L2(16).4",["unique almost simple group with the given socle and socle factor",[[17,8],[68,3],[120,5],[136,5]]]],
["L2(17)",["simple group",[[18,1],[102,1],[136,1],[153,1]]]],
["L2(17).2",["unique almost simple group with the given socle and socle factor",[[18,2],[136,2],[153,2]]]],
["L2(19)",["simple group",[[20,1],[57,1],[171,1],[190,1]]]],
["L2(19).2",["unique almost simple group with the given socle and socle factor",[[20,2],[171,2],[190,2],[285,1]]]],
["L2(23)",["simple group",[[24,2],[253,1],[253,3],[276,1]]]],
["L2(23).2",["unique almost simple group with the given socle and socle factor",[[24,3],[253,2],[276,2]]]],
["L2(25)",["simple group",[[26,1],[65,1],[300,1],[325,6]]]],
["L2(25).2^2",["unique almost simple group with the given socle and socle factor",[[26,5],[300,5],[325,10]]]],
["L2(25).2_1",["almost simple group with the given socle and socle factor that fits",[[26,2],[300,4],[325,9]]]],
["L2(25).2_2",["almost simple group with the given socle and socle factor that fits",[[26,3],[65,2],[300,2],[325,8]]]],
["L2(25).2_3",["almost simple group with the given socle and socle factor that fits",[[26,4],[300,3],[325,7]]]],
["L2(25)M3",["unique almost simple group with the given socle and socle factor",[[5,5],[6,2],[10,2]]]],
["L2(27)",["simple group",[[28,9],[351,1],[378,1],[819,1]]]],
["L2(27).2",["unique almost simple group with the given socle and socle factor",[[28,10],[351,2],[378,2],[819,2]]]],
["L2(27).3",["unique almost simple group with the given socle and socle factor",[[28,11],[351,3],[378,3],[819,3]]]],
["L2(27).6",["unique almost simple group with the given socle and socle factor",[[28,12],[351,4],[378,4],[819,4]]]],
["L2(29)",["simple group",[[30,1],[203,1],[406,1],[435,1]]]],
["L2(29).2",["unique almost simple group with the given socle and socle factor",[[30,2],[406,2],[435,2],[1015,1]]]],
["L2(31)",["simple group",[[32,4],[248,1],[465,1],[496,1],[620,1]]]],
["L2(31).2",["unique almost simple group with the given socle and socle factor",[[32,5],[465,2],[496,2]]]],
["L2(32)",["simple group",[[33,1],[496,6],[528,1]]]],
["L2(32).5",["unique almost simple group with the given socle and socle factor",[[33,2],[496,7],[528,2]]]],
["L2(37)",["simple group",[[38,1],[666,1],[703,1],[2109,1]]]],
["L2(41)",["simple group",[[42,1],[574,3],[820,1],[861,1],[1435,1]]]],
["L2(43)",["simple group",[[44,1],[903,1],[946,1],[3311,1]]]],
["L2(47)",["simple group",[[48,1],[1081,1],[1128,1],[2162,1]]]],
["L2(49)",["simple group",[[50,3],[175,1],[980,1],[1176,1],[1225,13]]]],
["L2(49).2^2",["unique almost simple group with the given socle and socle factor",[[50,7],[1176,5],[1225,17]]]],
["L2(49).2_1",["almost simple group with the given socle and socle factor that fits",[[50,4],[1176,4],[1225,15]]]],
["L2(49).2_2",["almost simple group with the given socle and socle factor that fits",[[50,5],[175,2],[980,2],[1176,3],[1225,16]]]],
["L2(49).2_3",["almost simple group with the given socle and socle factor that fits",[[50,6],[1176,2],[1225,14]]]],
["L2(53)",["simple group",[[54,1],[1378,1],[1431,1]]]],
["L2(59)",["simple group",[[60,6],[1711,1],[1711,2],[1770,1]]]],
["L2(61)",["simple group",[[62,1],[1830,1],[1891,1],[1891,2]]]],
["L2(64)",["simple group",[[65,8],[520,1],[2016,1],[2080,3]]]],
["L2(64).6",["unique almost simple group with the given socle and socle factor",[[65,11],[520,4],[2016,6],[2080,6]]]],
["L2(67)",["simple group",[[68,4],[2211,1],[2278,1]]]],
["L2(71)",["simple group",[[72,1],[2485,1],[2556,1],[2982,1]]]],
["L2(73)",["simple group",[[74,1],[2628,1],[2701,1]]]],
["L2(79)",["simple group",[[80,1],[3081,1],[3160,1]]]],
["L2(8)",["simple group",[[9,8],[28,2],[36,1]]]],
["L2(8).3",["unique almost simple group with the given socle and socle factor",[[9,9],[28,3],[36,2]]]],
["L2(81)",["simple group",[[82,1],[369,1],[3240,1],[3321,1]]]],
["L2(81).(2x4)",["unique almost simple group with the given socle and socle factor",[[82,8],[3240,8],[3321,8]]]],
["L2(81).2^2",["unique almost simple group with the given socle and socle factor",[[82,5],[3240,7],[3321,7]]]],
["L2(81).2_1",["almost simple group with the given socle and socle factor that fits",[[82,2],[369,2],[3240,2],[3321,3]]]],
["L2(81).2_2",["almost simple group with the given socle and socle factor that fits",[[82,3],[3240,4],[3321,4]]]],
["L2(81).2_3",["almost simple group with the given socle and socle factor that fits",[[82,4],[3240,3],[3321,2]]]],
["L2(81).4_1",["almost simple group with the given socle and socle factor that fits",[[82,6],[369,3],[3240,6],[3321,6]]]],
["L2(81).4_2",["almost simple group with the given socle and socle factor that fits",[[82,7],[3240,5],[3321,5]]]],
["L2(83)",["simple group",[[84,3],[3403,1],[3486,1]]]],
["L2(89)",["simple group",[[90,1],[3916,1],[4005,1]]]],
["L2(97)",["simple group",[[98,1]]]],
["L3(11)",["simple group",[[133,1]]]],
["L3(2)",["simple group",[[7,5],[8,4]]]],
["L3(2).2",["unique almost simple group with the given socle and socle factor",[[8,5],[21,1],[28,1]]]],
["L3(2)wr2",["hard test",[[49,34],[64,69],[168,3],[168,4]]]],
["L3(3)",["simple group",[[13,7],[144,1],[234,1]]]],
["L3(3).2",["unique almost simple group with the given socle and socle factor",[[52,1],[117,1],[144,2],[234,2]]]],
["L3(4)",["simple group",[[21,4],[56,1],[120,6],[280,3]]]],
["L3(4).2^2",["unique almost simple group with the given socle and socle factor",[[56,5],[105,3],[120,10],[280,8],[336,3]]]],
["L3(4).2_1",["almost simple group with the given socle and socle factor that fits",[[56,4],[105,2],[120,9],[280,6],[336,2]]]],
["L3(4).2_2",["almost simple group with the given socle and socle factor that fits",[[21,5],[56,2],[120,7],[280,5]]]],
["L3(4).2_3",["almost simple group with the given socle and socle factor that fits",[[56,3],[105,1],[120,8],[280,4],[336,1]]]],
["L3(4).3",["unique almost simple group with the given socle and socle factor",[[21,6],[280,7],[960,1]]]],
["L3(4).3.2_2",["almost simple group with the given socle and socle factor that fits",[[21,7],[280,10],[960,4]]]],
["L3(4).3.2_3",["almost simple group with the given socle and socle factor that fits",[[105,4],[280,9],[336,4],[960,3]]]],
["L3(4).6",["unique almost simple group with the given socle and socle factor",[[105,5],[280,11],[336,5],[960,2]]]],
["L3(4).D12",["unique almost simple group with the given socle and socle factor",[[105,6],[280,12],[336,6],[960,5]]]],
["L3(4)M4",["simple group",[[6,3],[10,3],[15,2]]]],
["L3(4)M5",["simple group",[[6,3],[10,3],[15,2]]]],
["L3(4)M7",["simple group",[[7,5],[8,4]]]],
["L3(4)M8",["simple group",[[7,5],[8,4]]]],
["L3(5)",["simple group",[[31,9],[3100,1],[3875,1],[4000,1]]]],
["L3(5).2",["unique almost simple group with the given socle and socle factor",[[186,1],[775,1],[3100,2],[3875,2],[4000,2]]]],
["L3(7)",["simple group",[[57,2]]]],
["L3(7).2",["unique almost simple group with the given socle and socle factor",[[456,1],[2793,1]]]],
["L3(7).3",["unique almost simple group with the given socle and socle factor",[[57,3]]]],
["L3(7).S3",["unique almost simple group with the given socle and socle factor",[[456,2],[2793,2]]]],
["L3(7)M2",["hard test",[[49,31]]]],
["L3(7)M4",["unique almost simple group with the given socle and socle factor",[[8,5],[21,1],[28,1]]]],
["L3(7)M5",["unique almost simple group with the given socle and socle factor",[[8,5],[21,1],[28,1]]]],
["L3(8)",["simple group",[[73,13]]]],
["L3(8).2",["unique almost simple group with the given socle and socle factor",[[657,1]]]],
["L3(8).3",["unique almost simple group with the given socle and socle factor",[[73,14]]]],
["L3(8).6",["unique almost simple group with the given socle and socle factor",[[657,2]]]],
["L3(9)",["simple group",[[91,7]]]],
["L3(9).2^2",["unique almost simple group with the given socle and socle factor",[[910,3]]]],
["L3(9).2_1",["almost simple group with the given socle and socle factor that fits",[[910,1]]]],
["L3(9).2_2",["almost simple group with the given socle and socle factor that fits",[[91,8]]]],
["L3(9).2_3",["almost simple group with the given socle and socle factor that fits",[[910,2]]]],
["L4(3)",["simple group",[[40,5],[117,2],[130,1],[2106,1]]]],
["L4(3).2^2",["unique almost simple group with the given socle and socle factor",[[130,5],[520,7],[1080,3],[2106,5]]]],
["L4(3).2_1",["almost simple group with the given socle and socle factor that fits",[[40,6],[130,3],[2106,2]]]],
["L4(3).2_2",["almost simple group with the given socle and socle factor that fits",[[117,3],[130,2],[520,5],[1080,2],[2106,4]]]],
["L4(3).2_3",["almost simple group with the given socle and socle factor that fits",[[130,4],[520,6],[1080,1],[2106,3]]]],
["L4(3)M4",["unique almost simple group with the given socle and socle factor",[[27,13],[36,9],[40,2],[40,4],[45,5]]]],
["L4(4)",["simple group",[[85,3],[357,1],[1008,3]]]],
["L4(4).2^2",["unique almost simple group with the given socle and socle factor",[[357,5],[1008,7],[1785,3]]]],
["L4(4).2_1",["almost simple group with the given socle and socle factor that fits",[[85,4],[357,3],[1008,4]]]],
["L4(4).2_2",["almost simple group with the given socle and socle factor that fits",[[357,4],[1008,6],[1785,2]]]],
["L4(4).2_3",["almost simple group with the given socle and socle factor that fits",[[357,2],[1008,5],[1785,1]]]],
["L4(5)",["simple group",[[156,5],[806,1],[1550,3]]]],
["L4(9)",["simple group",[[820,12]]]],
["L5(2)",["simple group",[[31,10],[155,1]]]],
["L5(2).2",["unique almost simple group with the given socle and socle factor",[[465,3],[496,8],[1085,1]]]],
["L5(3)",["simple group",[[121,49],[1210,1]]]],
["L6(2)",["simple group",[[63,6],[651,1],[1395,1]]]],
["L6(2).2",["unique almost simple group with the given socle and socle factor",[[1395,2],[1953,1],[2016,11]]]],
["L7(2)",["simple group",[[127,13],[2667,1]]]],
["L8(2)",["simple group",[[255,2]]]],
["LyM6",["hard test",[[243,29]]]],
["M11",["simple group",[[11,6],[12,1],[55,4],[66,2],[165,3]]]],
["M12",["simple group",[[12,2],[66,3],[144,3],[220,1],[396,1],[495,3],[495,5],[1320,1]]]],
["M12.2",["unique almost simple group with the given socle and socle factor",[[144,4],[144,5],[396,2],[495,4],[495,6],[880,1],[1320,2],[1584,1]]]],
["M12.2M3",["unique almost simple group with the given socle and socle factor",[[12,4],[55,2],[55,3],[66,1]]]],
["M12M2",["simple group",[[11,6],[12,1],[55,4],[66,2],[165,3]]]],
["M12M4",["unique almost simple group with the given socle and socle factor",[[10,7],[36,5],[45,3]]]],
["M12M7",["hard test",[[9,7]]]],
["M22",["simple group",[[22,1],[77,1],[176,3],[231,1],[330,1],[616,1],[672,5]]]],
["M22.2",["unique almost simple group with the given socle and socle factor",[[22,2],[77,2],[231,2],[330,2],[616,2],[672,6]]]],
["M22.2M3",["hard test",[[16,16]]]],
["M23",["simple group",[[23,5],[253,4],[253,5],[506,1],[1288,1],[1771,1]]]],
["M24",["simple group",[[24,1],[276,4],[759,1],[1288,2],[1771,2],[2024,1],[3795,1]]]],
["McL",["simple group",[[275,1],[2025,34]]]],
["McL.2",["unique almost simple group with the given socle and socle factor",[[275,2]]]],
["McLM10",["prim. group on solv. minimal normal subgroup",[[16,20]]]],
["McLM3",["simple group",[[22,1],[77,1],[176,3],[231,1],[330,1],[616,1],[672,5]]]],
["O10+(2)",["simple group",[[496,4],[527,1],[2295,2]]]],
["O10+(2).2",["unique almost simple group with the given socle and socle factor",[[496,5],[527,2]]]],
["O10+(2)M4",["prim. group on solv. minimal normal subgroup",[[1024,83]]]],
["O10-(2)",["simple group",[[495,1],[528,4]]]],
["O10-(2).2",["unique almost simple group with the given socle and socle factor",[[495,2],[528,5]]]],
["O12+(2)",["simple group",[[2016,14],[2079,1]]]],
["O12+(2).2",["unique almost simple group with the given socle and socle factor",[[2016,15],[2079,2]]]],
["O12-(2)",["simple group",[[2015,1],[2080,13]]]],
["O12-(2).2",["unique almost simple group with the given socle and socle factor",[[2015,2],[2080,14]]]],
["O7(3)",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O7(3).2",["unique almost simple group with the given socle and socle factor",[[351,6],[364,4],[378,6],[1120,6],[3640,4]]]],
["O7(3)M11",["unique almost simple group with the given socle and socle factor",[[9,11],[36,12],[84,2],[126,13],[280,2],[840,2]]]],
["O7(3)M5",["simple group",[[351,7],[364,5],[378,7],[2808,1],[3159,1],[3888,1]]]],
["O7(3)M8",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["O7(5)",["simple group",[[3906,4]]]],
["O7(5).2",["unique almost simple group with the given socle and socle factor",[[3906,6]]]],
["O8+(2)",["simple group",[[120,16],[135,2],[960,7],[1120,1],[1575,1]]]],
["O8+(2).2",["unique almost simple group with the given socle and socle factor",[[120,17],[135,3],[960,8],[1120,2],[1575,2],[2025,33]]]],
["O8+(2).3",["unique almost simple group with the given socle and socle factor",[[1575,3]]]],
["O8+(2).3.2",["unique almost simple group with the given socle and socle factor",[[1575,4]]]],
["O8+(2)M16",["hard test",[[25,24],[36,18],[60,5],[100,6]]]],
["O8+(2)M17",["hard test",[[25,24],[36,18],[60,5],[100,6]]]],
["O8+(2)M2",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["O8+(2)M3",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["O8+(2)M5",["prim. group on solv. minimal normal subgroup",[[64,59]]]],
["O8+(2)M6",["prim. group on solv. minimal normal subgroup",[[64,59]]]],
["O8+(2)M8",["simple group",[[9,10],[36,11],[84,1],[120,2],[126,12],[280,1],[840,1]]]],
["O8+(2)M9",["simple group",[[9,10],[36,11],[84,1],[120,2],[126,12],[280,1],[840,1]]]],
["O8+(3)",["simple group",[[1080,5],[1120,7]]]],
["O8+(3).(2^2)_{111}",["almost simple group with the given socle and socle factor that fits",[[1120,12]]]],
["O8+(3).(2^2)_{122}",["almost simple group with the given socle and socle factor that fits",[[1080,9],[1120,13]]]],
["O8+(3).2_1",["almost simple group with the given socle and socle factor that fits",[[1080,6],[1120,8],[1120,10]]]],
["O8+(3).2_1'",["almost simple group with the given socle and socle factor that fits",[[1080,6],[1120,8],[1120,10]]]],
["O8+(3).2_1''",["almost simple group with the given socle and socle factor that fits",[[1080,6],[1120,8],[1120,10]]]],
["O8+(3).2_2",["almost simple group with the given socle and socle factor that fits",[[1080,7],[1080,8],[1120,9]]]],
["O8+(3).2_2'",["almost simple group with the given socle and socle factor that fits",[[1080,7],[1080,8],[1120,9]]]],
["O8+(3).4",["unique almost simple group with the given socle and socle factor",[[1120,11]]]],
["O8+(3).D8",["unique almost simple group with the given socle and socle factor",[[1120,14]]]],
["O8+(3)M11",["simple group",[[120,16],[135,2],[960,7],[1120,1],[1575,1]]]],
["O8+(3)M12",["simple group",[[120,16],[135,2],[960,7],[1120,1],[1575,1]]]],
["O8+(3)M13",["simple group",[[120,16],[135,2],[960,7],[1120,1],[1575,1]]]],
["O8+(3)M2",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O8+(3)M25",["hard test",[[36,14],[100,19],[225,3],[360,11],[360,14]]]],
["O8+(3)M26",["hard test",[[36,14],[100,19],[225,3],[360,11],[360,14]]]],
["O8+(3)M3",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O8+(3)M4",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O8+(3)M5",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O8+(3)M6",["simple group",[[351,5],[364,3],[378,5],[1080,4],[1120,4],[3159,3],[3640,2]]]],
["O8+(3)M8",["prim. group on solv. minimal normal subgroup",[[729,468]]]],
["O8+(3)M9",["prim. group on solv. minimal normal subgroup",[[729,468]]]],
["O8-(2)",["simple group",[[119,1],[136,9],[765,1],[1071,1],[1632,1]]]],
["O8-(2).2",["unique almost simple group with the given socle and socle factor",[[119,2],[136,10],[765,2],[1071,2],[1632,2]]]],
["O8-(3)",["simple group",[[1066,1],[1107,1]]]],
["O8-(3).2^2",["unique almost simple group with the given socle and socle factor",[[1066,5]]]],
["O8-(3).2_1",["almost simple group with the given socle and socle factor that fits",[[1066,2],[1107,2]]]],
["O8-(3).2_2",["almost simple group with the given socle and socle factor that fits",[[1066,3]]]],
["O8-(3).2_3",["almost simple group with the given socle and socle factor that fits",[[1066,4]]]],
["O8-(3)M3",["unique almost simple group with the given socle and socle factor",[[351,6],[364,4],[378,6],[1120,6],[3640,4]]]],
["O9(3)",["simple group",[[3240,14],[3280,2],[3321,14]]]],
["ONM11",["simple group",[[11,6],[12,1],[55,4],[66,2],[165,3]]]],
["ONM2",["unique almost simple group with the given socle and socle factor",[[456,1],[2793,1]]]],
["ONM8",["simple group",[[32,4],[248,1],[465,1],[496,1],[620,1]]]],
["P1/G1/L1/V1/ext2",["prim. group on solv. minimal normal subgroup (classes test)",[[16,19]]]],
["P1/G1/L1/V1/ext3",["hard test",[[81,141]]]],
["P1/G3/L2/V1/ext3",["unique perfect group of its order",[[729,355]]]],
["P11/G1/L1/V1/ext3",["hard test",[[729,359]]]],
["P11/G2/L1/V1/ext3",["hard test",[[729,360]]]],
["P11/G3/L1/V1/ext3",["hard test",[[2187,19]]]],
["P11/G4/L1/V1/ext2",["hard test",[[256,136]]]],
["P13/G1/L2/V1/ext3",["hard test",[[2187,28]]]],
["P1L62",["prim. group on solv. minimal normal subgroup",[[32,3]]]],
["P1L82",["prim. group on solv. minimal normal subgroup",[[128,3]]]],
["P27/G1/L1/V1/ext2",["prim. group on solv. minimal normal subgroup",[[64,61]]]],
["P27/G1/L1/V1/ext3",["unique perfect group of its order",[[729,397]]]],
["P31/G1/L1/V1/ext3",["prim. group on solv. minimal normal subgroup",[[2187,43]]]],
["P41/G1/L1/V1/ext3",["hard test",[[2187,23]]]],
["P41/G2/L1/V1/ext2",["hard test",[[256,145]]]],
["P43/G1/L1/V1/ext2",["hard test",[[1024,52]]]],
["P43/G2/L1/V1/ext2",["hard test",[[1024,52]]]],
["P43/G3/L1/V1/ext2",["hard test",[[1024,51]]]],
["P48/G1/L1/V1/ext2",["hard test",[[1024,58]]]],
["P49/G1/L1/V1/ext3",["prim. group on solv. minimal normal subgroup",[[2187,35]]]],
["P50/G1/L1/V1/ext2",["prim. group on solv. minimal normal subgroup",[[64,57]]]],
["Ru",["simple group",[[4060,1]]]],
["S10(2)",["simple group",[[496,3],[528,3],[1023,1]]]],
["S12(2)",["simple group",[[2016,16],[2080,15],[4095,1]]]],
["S3",["prim. group on solv. minimal normal subgroup",[[3,2]]]],
["S3wrS4",["hard test",[[81,91]]]],
["S4(4)",["simple group",[[85,1],[120,12],[136,7],[1360,1]]]],
["S4(4).2",["unique almost simple group with the given socle and socle factor",[[85,2],[120,13],[136,8],[1360,2]]]],
["S4(4).2M5",["unique almost simple group with the given socle and socle factor",[[17,8],[68,3],[120,5],[136,5]]]],
["S4(4).2M7",["hard test",[[25,24],[36,18],[60,5],[100,6]]]],
["S4(4).4",["unique almost simple group with the given socle and socle factor",[[425,1],[1360,3]]]],
["S4(4)M4",["unique almost simple group with the given socle and socle factor",[[17,7],[68,2],[120,4],[136,4]]]],
["S4(4)M6",["hard test",[[25,23],[36,17],[60,3],[60,4],[100,5]]]],
["S4(5)",["simple group",[[156,1],[156,3],[300,6],[325,1]]]],
["S4(5).2",["unique almost simple group with the given socle and socle factor",[[156,2],[156,4],[300,7],[325,2]]]],
["S4(7)",["simple group",[[400,1],[400,3],[1176,6],[1225,18]]]],
["S4(7).2",["unique almost simple group with the given socle and socle factor",[[400,2],[400,4],[1176,7],[1225,19]]]],
["S4(8)",["simple group",[[585,1],[2016,9],[2080,9]]]],
["S4(8).3",["unique almost simple group with the given socle and socle factor",[[585,2],[2016,10],[2080,10]]]],
["S4(9)",["simple group",[[820,3],[820,8],[3240,9],[3321,9]]]],
["S4(9).2^2",["unique almost simple group with the given socle and socle factor",[[820,7],[820,24],[3240,13],[3321,13]]]],
["S4(9).2_1",["almost simple group with the given socle and socle factor that fits",[[820,5],[820,22],[3240,11],[3321,11]]]],
["S4(9).2_2",["almost simple group with the given socle and socle factor that fits",[[820,4],[820,9],[3240,12],[3321,12]]]],
["S4(9).2_3",["almost simple group with the given socle and socle factor that fits",[[820,6],[820,23],[3240,10],[3321,10]]]],
["S4wrS3",["hard test",[[64,39]]]],
["S6(2)",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["S6(3)",["simple group",[[364,1],[1120,3],[3640,1]]]],
["S6(3).2",["unique almost simple group with the given socle and socle factor",[[364,2],[1120,5],[3640,3]]]],
["S6(4)",["simple group",[[1365,7],[2016,12],[2080,11]]]],
["S6(4).2",["unique almost simple group with the given socle and socle factor",[[1365,8],[2016,13],[2080,12]]]],
["S6(5)",["simple group",[[3906,3]]]],
["S8(2)",["simple group",[[120,15],[136,6],[255,1],[2295,1]]]],
["S8(3)",["simple group",[[3280,1]]]],
["Suz",["simple group",[[1782,1]]]],
["Suz.2",["unique almost simple group with the given socle and socle factor",[[1782,2]]]],
["Symm(4)",["hard test",[[4,2]]]],
["Sz(32)",["simple group",[[1025,1]]]],
["Sz(32).5",["unique almost simple group with the given socle and socle factor",[[1025,2]]]],
["Sz(8)",["simple group",[[65,6],[560,1],[1456,1],[2080,1]]]],
["Sz(8).3",["unique almost simple group with the given socle and socle factor",[[65,7],[560,2],[1456,2],[2080,2]]]],
["U3(11)",["simple group",[[1332,1]]]],
["U3(11).2",["unique almost simple group with the given socle and socle factor",[[1332,2]]]],
["U3(11).3",["unique almost simple group with the given socle and socle factor",[[1332,3]]]],
["U3(11).S3",["unique almost simple group with the given socle and socle factor",[[1332,4]]]],
["U3(11)M4",["unique almost simple group with the given socle and socle factor",[[12,4],[55,2],[55,3],[66,1]]]],
["U3(11)M5",["unique almost simple group with the given socle and socle factor",[[12,4],[55,2],[55,3],[66,1]]]],
["U3(3)",["simple group",[[28,4],[36,6],[63,1],[63,3]]]],
["U3(3).2",["unique almost simple group with the given socle and socle factor",[[28,5],[36,7],[63,2],[63,4]]]],
["U3(4)",["simple group",[[65,3],[208,1],[416,1],[1600,17]]]],
["U3(4).2",["unique almost simple group with the given socle and socle factor",[[65,4],[208,2],[416,2],[1600,18]]]],
["U3(4).4",["unique almost simple group with the given socle and socle factor",[[65,5],[208,3],[416,3],[1600,19]]]],
["U3(5)",["simple group",[[50,1],[126,3],[175,3],[525,1]]]],
["U3(5).2",["unique almost simple group with the given socle and socle factor",[[50,2],[126,4],[175,4],[525,2],[750,1]]]],
["U3(5).3",["unique almost simple group with the given socle and socle factor",[[126,5],[525,3],[1750,1],[1750,2]]]],
["U3(5).3.2",["unique almost simple group with the given socle and socle factor",[[126,6],[525,4],[1750,3],[1750,4]]]],
["U3(5)M2",["simple group",[[7,6],[15,1],[21,2],[35,3]]]],
["U3(5)M3",["simple group",[[7,6],[15,1],[21,2],[35,3]]]],
["U3(5)M6",["almost simple group with the given socle and socle factor that fits",[[10,6],[36,3],[45,2]]]],
["U3(5)M7",["almost simple group with the given socle and socle factor that fits",[[10,6],[36,3],[45,2]]]],
["U3(7)",["simple group",[[344,1],[2107,1]]]],
["U3(7).2",["unique almost simple group with the given socle and socle factor",[[344,2],[2107,2]]]],
["U3(8)",["simple group",[[513,1],[3648,1]]]],
["U3(8).(S3x3)",["unique almost simple group with the given socle and socle factor",[[513,9],[3648,9]]]],
["U3(8).2",["unique almost simple group with the given socle and socle factor",[[513,2],[3648,2]]]],
["U3(8).3^2",["unique almost simple group with the given socle and socle factor",[[513,8],[3648,8]]]],
["U3(8).3_1",["almost simple group with the given socle and socle factor that fits",[[513,3],[3648,4]]]],
["U3(8).3_2",["almost simple group with the given socle and socle factor that fits",[[513,4],[3648,5]]]],
["U3(8).3_3",["almost simple group with the given socle and socle factor that fits",[[513,5],[3648,3]]]],
["U3(8).6",["unique almost simple group with the given socle and socle factor",[[513,6],[3648,6]]]],
["U3(8).S3",["unique almost simple group with the given socle and socle factor",[[513,7],[3648,7]]]],
["U3(8)M4",["hard test",[[9,6]]]],
["U3(8)M5",["hard test",[[9,6]]]],
["U3(9)",["simple group",[[730,1]]]],
["U3(9).2",["unique almost simple group with the given socle and socle factor",[[730,2]]]],
["U3(9).4",["unique almost simple group with the given socle and socle factor",[[730,3]]]],
["U4(2)",["simple group",[[27,12],[36,8],[40,1],[40,3],[45,4]]]],
["U4(2).2",["unique almost simple group with the given socle and socle factor",[[27,13],[36,9],[40,2],[40,4],[45,5]]]],
["U4(3)",["simple group",[[112,1],[126,7],[162,1],[280,13],[540,1],[567,1],[1296,132],[2835,1]]]],
["U4(3).(2^2)_{122}",["almost simple group with the given socle and socle factor that fits",[[112,5],[126,11],[280,17],[540,7],[567,5],[2835,7]]]],
["U4(3).(2^2)_{133}",["almost simple group with the given socle and socle factor that fits",[[112,7],[162,5],[280,19],[540,5],[2835,5]]]],
["U4(3).(2^2)_{133}M6",["unique almost simple group with the given socle and socle factor",[[56,5],[105,3],[120,10],[280,8],[336,3]]]],
["U4(3).2_1",["almost simple group with the given socle and socle factor that fits",[[112,3],[126,10],[162,4],[280,15],[540,3],[567,4],[2835,3]]]],
["U4(3).2_1M4",["unique almost simple group with the given socle and socle factor",[[27,13],[36,9],[40,2],[40,4],[45,5]]]],
["U4(3).2_2",["almost simple group with the given socle and socle factor that fits",[[112,2],[126,8],[126,9],[280,14],[540,4],[567,2],[567,3],[1296,133],[2835,4]]]],
["U4(3).2_2'",["almost simple group with the given socle and socle factor that fits",[[112,2],[126,8],[126,9],[280,14],[540,4],[567,2],[567,3],[1296,133],[2835,4]]]],
["U4(3).2_3",["almost simple group with the given socle and socle factor that fits",[[112,4],[162,2],[162,3],[280,16],[540,2],[2835,2]]]],
["U4(3).2_3'",["almost simple group with the given socle and socle factor that fits",[[112,4],[162,2],[162,3],[280,16],[540,2],[2835,2]]]],
["U4(3).2_3M10",["unique almost simple group with the given socle and socle factor",[[10,7],[36,5],[45,3]]]],
["U4(3).4",["unique almost simple group with the given socle and socle factor",[[112,6],[280,18],[540,6],[2835,6]]]],
["U4(3).D8",["unique almost simple group with the given socle and socle factor",[[112,8],[280,20],[540,8],[2835,8]]]],
["U4(3)M12",["simple group",[[7,6],[15,1],[21,2],[35,3]]]],
["U4(3)M3",["simple group",[[27,12],[36,8],[40,1],[40,3],[45,4]]]],
["U4(3)M9",["unique perfect group of its order",[[16,17]]]],
["U4(4)",["simple group",[[325,3],[1040,2],[1105,3],[3264,1]]]],
["U4(4).4",["unique almost simple group with the given socle and socle factor",[[325,5],[1040,5],[1105,5],[3264,3]]]],
["U4(5)",["simple group",[[756,1],[1575,7],[3276,1]]]],
["U4(5).2^2",["unique almost simple group with the given socle and socle factor",[[756,5],[3276,5]]]],
["U4(5).2_1",["almost simple group with the given socle and socle factor that fits",[[756,3],[1575,8],[3276,4]]]],
["U4(5).2_2",["almost simple group with the given socle and socle factor that fits",[[756,4],[3276,2]]]],
["U4(5).2_3",["almost simple group with the given socle and socle factor that fits",[[756,2],[3276,3]]]],
["U5(2)",["simple group",[[165,1],[176,1],[297,1],[1408,1],[3520,1]]]],
["U5(2).2",["unique almost simple group with the given socle and socle factor",[[165,2],[176,2],[297,2],[1408,2],[3520,2]]]],
["U5(3)",["simple group",[[2440,1]]]],
["U6(2)",["simple group",[[672,1],[693,1],[891,1],[1408,3]]]],
["U6(2).2",["unique almost simple group with the given socle and socle factor",[[672,2],[693,2],[891,2],[1408,4]]]],
["U6(2).3",["unique almost simple group with the given socle and socle factor",[[672,3],[693,3],[891,3]]]],
["U6(2).3.2",["unique almost simple group with the given socle and socle factor",[[672,4],[693,4],[891,4]]]],
["U6(2)M10",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["U6(2)M12",["simple group",[[22,1],[77,1],[176,3],[231,1],[330,1],[616,1],[672,5]]]],
["U6(2)M13",["simple group",[[22,1],[77,1],[176,3],[231,1],[330,1],[616,1],[672,5]]]],
["U6(2)M5",["almost simple group with the given socle and socle factor that fits",[[112,2],[126,8],[126,9],[280,14],[540,4],[567,2],[567,3],[1296,133],[2835,4]]]],
["U6(2)M6",["almost simple group with the given socle and socle factor that fits",[[112,2],[126,8],[126,9],[280,14],[540,4],[567,2],[567,3],[1296,133],[2835,4]]]],
["U6(2)M9",["simple group",[[28,6],[36,10],[63,5],[120,14],[135,1],[315,1],[336,7],[960,6]]]],
["U7(2)",["simple group",[[2709,1],[2752,9]]]],
["a4",["prim. group on solv. minimal normal subgroup",[[4,1]]]],
["a5wc2",["hard test",[[25,23],[36,17],[60,3],[60,4],[100,5]]]],
["affine",["hard test",[[81,129]]]],
["frob",["prim. group on solv. minimal normal subgroup",[[29,6]]]],
["g61",["hard test",[[625,497],[625,498]]]],
["j3m4",["hard test",[[16,14]]]],
["mo61",["hard test",[[16,10]]]],
["mo62",["prim. group on solv. minimal normal subgroup (classes test)",[[16,18]]]],
["mo62p",["prim. group on solv. minimal normal subgroup (classes test)",[[16,19]]]],
["mo81",["prim. group on solv. minimal normal subgroup",[[64,58]]]],
["mx1j4",["prim. group on solv. minimal normal subgroup (classes test)",[[2048,11]]]],
["s3wrs2",["hard test",[[9,2]]]],
["s3wrs3",["hard test",[[27,8]]]],
["s4",["hard test",[[4,2]]]],
["s4wrs2",["hard test",[[16,10]]]],
["s5wrs2",["hard test",[[25,26],[36,20],[100,8]]]],
["w(d5)",["prim. group on solv. minimal normal subgroup (classes test)",[[16,18]]]]
],
"nonautomatic": [
["(A6xA6xA6).(2xS4)",["hard test",[[1000,75]]]],
["2^10:(L5(2)xS3)",["added by hand",[[1024,91]]]],
["3^6.L4(3).D8",["added by hand",[[729,483]]]],
["5^4:(3x2.L2(25)).2",["hard test",[[625,670]]]],
["P2L62",["added by hand",[[256,212]]]],
["P3L62",["added by hand",[[512,47]]]]
]
}
[ Dauer der Verarbeitung: 0.15 Sekunden
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]
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