Quelle  grp_indiv.json   Sprache: unbekannt

{
"version": "01-May-2025, 05:40:21 UTC",
"idenum": "CTblLib.Data.IdEnumerator",
"attrid": "indiv",
"automatic": [
],
"nonautomatic": [
["(L3(2)xL3(4)).2",[
["IndividualGroupConstruction","perms",
[[2,3,7,4,8,6,5,1,61,23,55,33,43,17,45,59,63,47,21,42,35,26,40,19,37,31,16,15,11,60,56,13,44,10,39,29,9,52,18,53,46,48,49,62,27,58,57,64,32,34,41,28,30,12,25,20,24,51,38,50,36,14,54,22],
[6,2,1,3,7,8,4,5,61,59,12,26,63,49,13,48,43,52,55,57,9,39,18,23,47,16,40,51,64,25,56,41,15,45,53,42,27,54,31,33,60,19,11,34,24,21,20,17,36,14,10,44,30,58,50,29,35,28,38,46,32,22,37,62]],
"subdirect product of L3(2).2 and L3(4).2_1"]]],
["(L3(2)xL3(4).2_2).2",[
["IndividualGroupConstruction","perms",
[[1,2,10,6,3,9,7,8,5,4,113,84,75,87,51,118,96,48,53,57,78,26,82,16,97,70,13,62,14,66,108,39,67,11,88,42,104,103,64,81,63,21,71,76,45,60,12,46,35,54,105,61,89,95,65,122,32,93,33,79,38,15,40,22,114,30,23,121,56,20,59,111,37,17,34,41,44,31,92,107,101,100,55,68,80,27,58,47,91,120,109,90,69,74,19,85,72,110,86,43,77,36,52,106,24,73,112,115,50,119,25,94,99,116,102,98,117,28,83,18,49,29],
[2,1,4,9,8,7,5,10,6,3,76,52,93,88,58,38,79,107,61,50,104,71,57,101,66,99,74,63,113,51,82,46,110,112,103,120,85,15,72,12,62,19,42,95,92,81,22,45,44,96,77,49,64,14,28,24,121,33,36,31,109,87,118,60,100,25,83,69,89,18,117,70,116,68,32,90,105,54,39,11,27,114,73,41,47,29,97,80,102,26,40,17,34,37,21,86,56,106,78,122,35,75,84,115,98,55,48,67,108,111,65,53,119,13,91,43,23,30,59,20,94,16]],
"subdirect product of L3(2).2 and L3(4).2^2"]]],
["12.A6.2_3",[
["IndividualGroupConstruction","perms",
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[3,6,9,10,12,7,13,15,18,19,20,22,11,4,25,26,28,31,32,2,34,36,5,38,41,42,43,40,27,47,50,51,1,53,44,55,57,60,37,24,21,61,39,62,16,64,67,46,69,71,72,58,45,65,74,33,76,77,23,79,8,52,35,81,82,29,75,84,86,68,14,59,85,56,88,63,89,90,66,17,87,78,54,48,83,30,73,70,80,49,93,95,97,99,94,101,103,104,106,108,110,112,114,116,117,118,92,120,122,109,124,126,102,115,128,130,132,123,134,136,138,105,96,121,139,140,141,142,144,146,98,107,131,125,119,148,100,147,150,152,91,137,113,154,156,149,158,127,111,160,133,153,162,164,165,166,161,168,170,143,159,135,167,169,129,157,155,151,145,163],
[4,7,10,5,1,13,11,16,19,12,2,3,20,23,26,21,29,32,22,6,8,9,33,39,42,34,44,27,35,48,51,36,14,15,17,18,58,37,52,43,61,53,62,28,41,65,46,54,70,72,55,24,25,30,31,71,77,38,56,57,45,40,80,82,47,63,64,85,68,73,59,74,49,50,81,89,60,75,76,66,78,67,86,83,69,84,90,87,79,88,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170]],
"subdirect product of 3.A6.2_3 and 4.A6.2_3"]]],
["12_1.L3(4).2_2",[
["IndividualGroupConstruction","perms",
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"subdirect product of 4_1.L3(4).2_2 and 3.L3(4).2_2"]]],
["12_1.L3(4).2_3",[
["IndividualGroupConstruction","perms",
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"subdirect product of 4_1.L3(4).2_3 and 3.L3(4).2_3"]]],
["12_1.U4(3)",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_1.U4(3) and 4.U4(3)"]]],
["12_1.U4(3).2_1",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_1.U4(3).2_1 and 4.U4(3).2_1"]]],
["12_1.U4(3).2_2",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_1.U4(3).2_2 and 4.U4(3).2_2"]]],
["12_1.U4(3).2_2'",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_1.U4(3).2_2' and 4.U4(3).2_2"]]],
["12_2.L3(4).2_2",[
["IndividualGroupConstruction","perms",
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[1,3,2,6,8,4,10,5,13,7,16,17,9,20,15,11,12,21,26,14,18,29,31,33,25,19,37,34,22,41,23,43,24,28,42,46,27,48,47,49,30,35,32,51,53,36,39,38,40,50,44,52,45,60,61,56,62,58,63,54,55,57,59,64,65,66,67,78,69,154,191,158,127,197,140,200,183,68,113,111,102,146,121,164,162,109,168,177,139,176,175,171,170,169,112,174,189,202,194,100,165,81,166,104,181,195,198,167,86,173,80,95,79,172,160,190,185,128,161,120,83,178,123,186,199,188,73,118,156,203,131,155,159,196,135,193,137,180,89,75,187,192,144,143,163,82,184,179,150,149,201,182,157,70,132,129,153,72,133,115,119,85,145,84,101,103,108,87,94,93,92,114,110,96,91,90,88,122,148,138,105,152,77,147,117,124,141,126,97,116,71,142,136,99,106,134,74,107,125,76,151,98,130,218,242,206,207,208,209,252,269,241,216,259,245,213,266,204,219,282,221,264,248,243,276,231,232,268,236,277,226,227,272,267,235,229,283,238,265,240,212,205,224,278,215,280,247,223,250,249,273,210,254,253,275,256,257,281,214,274,279,270,263,222,239,217,234,228,211,262,271,233,251,260,255,225,230,244,261,246,258,220,237,286,285,284,287]],
"subdirect product of 4_2.L3(4).2_2 and 3.L3(4).2_2"]]],
["12_2.L3(4).2_3",[
["IndividualGroupConstruction","perms",
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"subdirect product of 4_2.L3(4).2_3 and 3.L3(4).2_3"]]],
["12_2.U4(3)",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_2.U4(3) and 4.U4(3)"]]],
["12_2.U4(3).2_1",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_2.U4(3).2_1 and 4.U4(3).2_1"]]],
["12_2.U4(3).2_3",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_2.U4(3).2_3 and 4.U4(3).2_3"]]],
["12_2.U4(3).2_3'",[
["IndividualGroupConstruction","perms",
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"subdirect product of 3_2.U4(3).2_3' and 4.U4(3).2_3"]]],
["2.2^(2+2).2^(1+1+2+2):S4",[
["IndividualGroupConstruction","codepcgroup",
1930501744135702760007924063779493147723485323648989510005835339650309712951844578561807595852857245710326977530089008298621642033852786660914150705636512939089932968121672427843302854036094276455762844557574196879792698935109222024544735239306118996971586589040506656149330101547007097564906474937484681327715056659881264603521342490742365492865241139149158100570925722339271569265791573759213670146048,49152]]],
["2.L2(11).2",[
["IndividualGroupConstruction","ffmats",
["6 121 2 2\n2\n0\n0\n6\n",
"6 121 2 2\n10\n1\n10\n0\n",
"6 121 2 2\n47\n0\n0\n85\n"],
"index 5 subgroup in the isoclinic variant of GL(2,11)"]]],
["2.L2(19).2",[
["IndividualGroupConstruction","ffmats",
["6 361 2 2\n2\n0\n0\n10\n",
"6 361 2 2\n18\n1\n18\n0\n",
"6 361 2 2\n102\n0\n0\n278\n"],
"index 9 subgroup in the isoclinic variant of GL(2,19)"]]],
["2.L2(23).2",[
["IndividualGroupConstruction","ffmats",
["6 529 2 2\n5\n0\n0\n14\n",
"6 529 2 2\n22\n1\n22\n0\n",
"6 529 2 2\n265\n0\n0\n287\n"],
"index 11 subgroup in the isoclinic variant of GL(2,23)"]]],
["2.L2(25).2_1",[
["IndividualGroupConstruction","ffmats",
["6 625 2 2\n158\n0\n0\n314\n",
"6 625 2 2\n4\n605\n598\n0\n",
"6 625 2 2\n605\n0\n0\n182\n"],
"index 13 subgroup in the isoclinic variant of GU(2,25)"]]],
["2.L2(27).2",[
["IndividualGroupConstruction","ffmats",
["6 729 2 2\n650\n0\n0\n191\n",
"6 729 2 2\n2\n1\n2\n0\n",
"6 729 2 2\n291\n0\n0\n555\n"],
"index 13 subgroup in the isoclinic variant of GL(2,27)"]]],
["2.L2(27).6",[
["IndividualGroupConstruction","ffmats",
["1 9 6 6\n010000\n001000\n210000\n000102\n000100\n000010\n",
"1 9 6 6\n200100\n020010\n002001\n200000\n020000\n002000\n",
"1 9 6 6\n100000\n210000\n111000\n000100\n000210\n000111\n",
"1 9 6 6\n800000\n080000\n008000\n000400\n000040\n000004\n"],
"index 13 subgroup in the isoclinic variant of GammaL(2,27)"]]],
["2.L2(29).2",[
["IndividualGroupConstruction","ffmats",
["6 841 2 2\n2\n0\n0\n15\n",
"6 841 2 2\n28\n82\n147\n0\n",
"6 841 2 2\n788\n0\n0\n147\n"],
"index 15 subgroup in the isoclinic variant of GU(2,29)"]]],
["2.L2(31).2",[
["IndividualGroupConstruction","ffmats",
["6 961 2 2\n3\n0\n0\n21\n",
"6 961 2 2\n30\n1\n30\n0\n",
"6 961 2 2\n841\n0\n0\n151\n"],
"index 15 subgroup in the isoclinic variant of GL(2,31)"]]],
["2.L3(4).2_3",[
["IndividualGroupConstruction","perms",
[[33,72,34,71,78,77,95,96,2,4,5,6,59,60,79,80,100,99,49,50,55,56,88,87,14,13,28,27,102,101,110,109,90,89,105,106,103,104,82,81,21,22,20,19,83,84,48,47,43,44,24,23,35,36,42,41,111,112,25,26,45,46,32,31,29,30,15,16,17,18,9,10,37,38,40,39,11,12,68,67,76,75,62,61,94,93,52,51,1,3,86,85,92,91,107,108,58,57,69,70,65,66,74,73,54,53,8,7,64,63,97,98],
[46,97,45,98,3,1,109,110,107,108,64,63,27,28,22,21,102,101,100,99,44,43,26,25,31,32,9,10,18,17,76,75,105,106,50,49,60,59,20,19,104,103,40,39,55,56,68,67,14,13,23,24,89,90,65,66,11,12,72,71,77,78,82,81,85,86,48,47,7,8,38,37,92,91,83,84,42,41,70,69,2,4,51,52,5,6,111,112,87,88,61,62,80,79,94,93,57,58,16,15,30,29,74,73,54,53,35,36,96,95,34,33]],
"factor group of 4_1.L3(4).2_3"]]],
["2.L4(3).2_2",[
["IndividualGroupConstruction","perms",
[[13,34,31,49,38,75,6,62,12,8,26,61,14,41,25,57,21,3,22,77,79,43,5,32,4,2,29,10,20,70,74,30,72,55,46,80,1,52,33,35,37,23,36,68,58,71,15,53,47,40,9,42,17,7,11,51,45,73,78,54,56,66,65,24,59,28,63,39,27,64,50,44,16,76,60,18,69,67,48,19,153,126,149,87,97,160,94,140,98,136,129,138,110,103,119,117,112,114,146,134,124,142,155,113,158,118,137,120,156,81,89,128,148,141,143,83,107,145,88,125,159,135,122,150,82,108,151,144,101,147,86,90,121,116,99,109,154,131,95,139,111,157,133,85,105,123,104,130,100,91,102,93,152,96,84,132,127,106,115,92],
[137,90,146,85,149,142,152,147,138,88,134,132,128,119,125,93,151,81,118,133,148,159,129,105,160,141,110,114,124,104,153,117,99,113,95,120,82,156,122,107,123,97,115,109,157,111,116,121,127,84,136,130,91,108,150,100,89,158,131,98,140,94,126,96,135,143,87,92,145,139,144,154,103,83,112,102,106,86,101,155,5,73,56,78,65,63,55,40,25,58,46,39,36,9,64,34,3,30,69,60,4,62,37,21,44,8,52,43,42,13,32,31,6,19,80,20,12,79,45,38,76,47,59,26,48,54,7,66,41,49,2,75,77,10,51,28,67,70,15,17,24,18,72,74,33,29,68,71,35,16,61,11,53,57,50,1,14,22,23,27]],
"semidirect product of 2.L4(3) with an outer automorphism"]]],
["2.L4(3).2_3",[
["IndividualGroupConstruction","perms",
[[65,135,108,124,97,151,158,131,104,126,99,153,142,115,88,95,149,122,144,117,90,106,160,133,113,86,140,120,93,147,154,127,100,89,143,116,138,111,84,91,145,118,134,107,1,102,156,129,109,82,136,152,125,98,159,132,105,85,139,112,119,92,146,96,150,123,130,103,157,137,110,83,114,87,141,148,121,94,101,155,128,58,34,29,5,62,57,33,9,31,7,55,59,35,2,6,63,30,61,28,4,8,56,32,36,3,60,23,80,47,51,27,75,76,52,19,53,20,77,81,48,24,25,73,49,74,50,26,21,78,54,46,22,79,18,66,42,43,10,67,71,38,14,39,15,72,64,40,16,11,68,44,69,45,12,13,70,37,41,17],
[136,24,17,42,35,46,80,64,60,67,63,74,27,11,4,29,49,45,52,39,32,57,77,70,14,7,21,81,65,58,2,22,18,40,36,47,30,50,43,68,61,75,25,12,5,15,8,19,53,37,33,55,78,71,41,34,48,79,66,59,3,23,16,26,10,6,28,51,44,69,62,73,56,76,72,13,9,20,54,38,31,114,138,150,93,117,129,153,105,126,159,102,87,111,135,147,90,123,144,96,120,132,156,99,84,108,141,89,113,137,149,92,125,128,1,104,134,158,101,86,110,143,146,98,122,152,95,119,131,155,107,83,116,140,85,109,142,145,97,121,133,157,100,130,154,106,82,115,139,151,94,118,148,91,124,127,160,103,88,112]],
"semidirect product of 2.L4(3) with an outer automorphism"]]],
["2.O8+(2)",[
["IndividualGroupConstruction","perms",
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"derived subgroup of the Weyl group of type E8"]]],
["2.O8+(2).2",[
["IndividualGroupConstruction","perms",
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"Weyl group of type E8"]]],
["2.S4(5).2",[
["IndividualGroupConstruction","perms",
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"semidirect product of 2.S4(5) with an outer automorphism"]]],
["2.U4(3)",[
["IndividualGroupConstruction","perms",
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[83,84,3,4,82,81,85,86,46,45,200,199,32,31,135,136,90,89,220,219,64,63,191,192,17,18,180,179,74,73,158,157,116,115,114,113,111,112,1,2,5,6,7,8,22,21,172,171,196,195,93,94,95,96,98,97,36,35,37,38,34,33,160,159,202,201,105,106,101,102,11,12,221,222,152,151,107,108,203,204,43,44,42,41,39,40,71,72,178,177,155,156,123,124,125,126,128,127,216,215,138,137,91,92,194,193,174,173,26,25,61,62,60,59,58,57,147,148,67,68,20,19,55,56,52,51,54,53,132,131,134,133,129,130,142,141,118,117,210,209,150,149,78,77,165,166,50,49,47,48,69,70,16,15,190,189,65,66,175,176,153,154,140,139,218,217,87,88,13,14,223,224,104,103,163,164,185,186,80,79,212,211,187,188,181,182,30,29,197,198,28,27,167,168,76,75,143,144,119,120,145,146,214,213,121,122,109,110,9,10,207,208,99,100,24,23,169,170,183,184,205,206,161,162]],
"a factor group of SU(4,3)"]]],
["2.U4(3).2_1",[
["IndividualGroupConstruction","ffmats",
["1 9 6 6\n800000\n080000\n000440\n008840\n004840\n000004\n",
"1 9 6 6\n840800\n080000\n000044\n040400\n008084\n004084\n",
"1 9 6 6\n120200\n220120\n001000\n000001\n020100\n210110\n"],
"isoclinic variant of SO(-1,6,3)"]]],
["2.U4(3).2_3",[
["IndividualGroupConstruction","perms",
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"isoclinic variant of a subgroup of 2.U4(3).D8"]]],
["2.U4(3).4",[
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"a factor group of GU(4,3)"]]],
["2E6(2).2N3C",[
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["2^(2+1+2).2^(1+1+2).2^2.S4",[
["IndividualGroupConstruction","codepcgroup",
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["2^(4+10).(S4xS3)",[
["IndividualGroupConstruction","codepcgroup",
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["2^11.2^6.3^(1+2).D8",[
["IndividualGroupConstruction","codepcgroup",
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["2^12:J2",[
["IndividualGroupConstruction","perms",
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"semidirect product of 2^12 with J2 (see book CTblLibXpls)"]]],
["2^12:Sz(8)",[
["IndividualGroupConstruction","perms",
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"semidirect product of 2^12 with Sz(8) (see book CTblLibXpls)"]]],
["2^2.O8+(2)",[
["IndividualGroupConstruction","perms",
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"contributed by Alexander Hulpke"]]],
["2^2.O8+(3)",[
["IndividualGroupConstruction","ffmats",
["1 3 16 16\n1000000000000000\n0110000000000000\n0010000000000000\n0001000000000000\n0000100000000000\n0000011000000000\n0000001000000000\n0000000100000000\n0000000010000000\n0000000001100000\n0000000000100000\n0000000000010000\n0000000000001000\n0000000000000110\n0000000000000010\n0000000000000001\n",
"1 3 16 16\n1000000000000000\n0100000000000000\n0010100000000000\n0001010000000000\n0000100000000000\n0000010000000000\n0000001000000000\n0000000100000000\n0000000012000000\n0000000001000000\n0000000000100000\n0000000000010000\n0000000000001000\n0000000000000100\n0000000000000012\n0000000000000001\n",
"1 3 16 16\n1000000000000000\n2100000000000000\n0010000000000000\n0001000000000000\n0000100000000000\n0000010000000000\n0000001000000000\n0000002100000000\n0000000010000000\n0000000001000000\n0000000000100000\n0000000000010000\n0000000000101000\n0000000000010100\n0000000000000010\n0000000000000001\n", 
"1 3 16 16\n1000000000000000\n0100000000000000\n0011000000000000\n0001000000000000\n0000110000000000\n0000010000000000\n0000001000000000\n0000000100000000\n0000000010000000\n0000000001000000\n0000000000110000\n0000000000010000\n0000000000001100\n0000000000000100\n0000000000000010\n0000000000000001\n",
"1 3 16 16\n1000000000000000\n0100000000000000\n0010000000000000\n0011000000000000\n0000100000000000\n0000110000000000\n0000001000000000\n0000000100000000\n0000000010000000\n0000000001000000\n0000000000100000\n0000000000110000\n0000000000001000\n0000000000001100\n0000000000000010\n0000000000000001\n",
"1 3 16 16\n1000000000000000\n0100000000000000\n0110000000000000\n0001000000000000\n0000100000000000\n0000010000000000\n0000011000000000\n0000000100000000\n0000000010000000\n0000000001000000\n0000000001100000\n0000000000010000\n0000000000001000\n0000000000000100\n0000000000000110\n0000000000000001\n",
"1 3 16 16\n1000000000000000\n0100000000000000\n0010000000000000\n0001000000000000\n0010100000000000\n0001010000000000\n0000001000000000\n0000000100000000\n0000000010000000\n0000000021000000\n0000000000100000\n0000000000010000\n0000000000001000\n0000000000000100\n0000000000000010\n0000000000000021\n",
"1 3 16 16\n1200000000000000\n0100000000000000\n0010000000000000\n0001000000000000\n0000100000000000\n0000010000000000\n0000001200000000\n0000000100000000\n0000000010000000\n0000000001000000\n0000000000101000\n0000000000010100\n0000000000001000\n0000000000000100\n0000000000000010\n0000000000000001\n"],
"subgroup of GL(16,3)"]]],
["3.L3(4).6",[
["IndividualGroupConstruction","perms",
[[2,5,8,11,1,16,19,21,9,25,28,31,34,6,38,14,43,45,47,50,3,22,57,59,61,63,66,4,20,44,60,46,70,65,74,39,42,78,81,83,86,76,80,89,90,54,7,95,40,29,64,96,53,32,24,26,73,92,55,12,10,62,56,102,13,105,107,68,71,108,110,111,23,101,103,37,52,15,115,17,36,114,49,118,85,94,117,120,30,18,67,97,79,41,123,77,58,124,84,109,35,51,122,98,27,113,91,33,119,69,125,87,126,116,93,82,112,99,100,121,88,75,48,104,72,106],
[3,6,9,12,14,17,20,22,24,26,29,32,35,34,39,41,44,46,48,51,53,55,58,16,62,64,1,37,60,67,61,68,71,72,75,11,31,79,82,84,27,38,87,74,10,92,93,90,5,95,28,94,59,47,96,4,85,76,69,23,7,100,81,50,104,30,108,109,43,21,86,112,63,40,8,36,80,114,116,107,42,54,117,2,119,118,70,15,33,57,89,121,88,83,120,13,78,122,49,113,91,18,52,66,111,56,105,110,106,65,98,99,97,25,123,73,124,101,126,45,115,77,102,125,103,19],
[4,7,10,13,15,18,3,23,19,27,30,33,36,37,40,42,39,9,49,52,54,56,35,60,16,65,64,34,66,62,22,69,11,73,76,77,1,80,74,85,50,84,88,25,91,59,94,41,20,14,67,31,97,87,82,98,96,17,45,99,24,101,8,103,29,106,109,105,51,48,102,26,55,113,78,108,79,43,75,46,110,111,57,100,112,61,93,71,121,122,123,21,2,120,124,115,89,81,28,83,114,70,63,32,12,107,58,92,44,116,38,90,118,5,125,53,126,47,104,117,6,95,86,68,119,72]],
"semidirect product of SL(3,4) with an outer automorphism of order 6"]]],
["3.L3(7).3",[
["IndividualGroupConstruction","ffmats",
["1 7 3 3\n300\n050\n001\n",
"1 7 3 3\n601\n600\n060\n",
"1 7 3 3\n200\n010\n001\n"],
"index 2 subgroup in GL(3,7)"]]],
["3.U3(11).3",[
["IndividualGroupConstruction","ffmats",
["6 121 3 3\n11\n0\n0\n0\n106\n0\n0\n0\n66\n",
"6 121 3 3\n88\n10\n1\n10\n10\n0\n1\n0\n0\n",
"6 121 3 3\n49\n0\n0\n0\n1\n0\n0\n0\n34\n"],
"index 4 subgroup in GU(3,11)"]]],
["3.U3(5).3",[
["IndividualGroupConstruction","ffmats",
["6 25 3 3\n5\n0\n0\n0\n12\n0\n0\n0\n15\n",
"6 25 3 3\n20\n4\n1\n4\n4\n0\n1\n0\n0\n",
"6 25 3 3\n11\n0\n0\n0\n1\n0\n0\n0\n11\n"],
"index 2 subgroup of GU(3,8)"]]],
["3.U3(8).2",[
["IndividualGroupConstruction","perms",
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