Finite Group DatabasebetaFinite Group Databasebeta| order | 13149 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C487 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #17983940 |
| commutator, hypocenter | C487 | C27 |
| Fitting, socle, prime radical | C3×C487 | C9 |
| cosocle | #17983938 | C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 514 |
| transitive degree | μt(G) = 13149 |
A minimal faithful permutation representation — 2 generators on 514 points:
(2,3,6,4,7,14,9,16,33)(5,11,25,12,26,57,28,59,126)(8,18,41,19,42,92,44,94,75)(10,22,51,23,52,115,21,49,111)(13,30,68,31,69,149,71,151,285)(15,35,78,32,73,158,60,37,83)(17,38,85,39,86,34,76,163,77)(20,46,103,47,104,212,106,213,251)(24,54,121,55,122,243,64,141,276)(27,61,133,62,134,215,136,105,162)(29,65,143,66,144,279,50,113,227)(36,80,170,81,171,312,173,131,261)(40,89,187,90,188,127,190,330,252)(43,96,161,97,200,273,202,196,177)(45,100,207,101,208,230,164,304,375)(48,108,209,109,220,354,222,338,427)(53,118,235,119,236,193,238,382,165)(56,124,248,125,249,397,154,293,292)(58,128,199,129,254,340,256,84,178)(63,138,269,139,270,414,272,415,399)(67,146,70,147,283,98,142,277,204)(72,155,295,156,296,250,114,229,374)(74,160,301,137,117,232,180,233,376)(79,167,176,168,308,214,99,102,210)(82,174,316,175,317,419,318,288,431)(87,182,321,183,95,197,324,198,181)(88,184,116,185,325,231,159,299,341)(91,192,334,153,290,286,291,432,428)(93,194,253,195,335,401,132,112,226)(107,217,360,218,361,422,305,438,472)(110,224,307,152,289,145,281,424,166)(120,240,387,241,388,357,390,477,400)(123,245,394,246,395,358,396,271,306)(130,258,287,259,407,336,179,262,150)(135,266,348,267,379,459,319,337,320)(140,274,417,275,418,470,260,409,482)(148,268,221,284,172,314,294,315,445)(157,298,331,265,365,451,278,322,189)(169,309,410,310,441,416,216,359,421)(186,327,244,328,450,393,402,369,466)(191,332,280,333,452,423,300,436,430)(201,343,406,344,433,481,345,211,356)(203,346,247,347,353,378,323,447,471)(205,349,362,350,219,363,225,364,465)(206,351,371,255,355,444,403,463,478)(223,367,242,368,458,391,439,462,476)(228,372,264,373,429,411,449,389,263)(234,380,329,381,366,257,404,311,405)(237,383,448,384,342,455,474,339,326)(239,385,352,386,475,377,302,437,460)(282,426,479,303,392,464,420,398,480)(297,434,469,435,413,370,467,408,440)(313,442,456,443,446,454,453,425,484)(412,483,485,473,487,486,457,461,468)(488,489,492,490,493,498,495,500,505,491,494,499,496,501,506,503,508,511,497,502,507,504,509,512,510,513,514);(1,2,5,13,32,74,161,303,259,89,189,309,233,379,472,332,453,229,133,264,156,28,64,142,278,411,92,193,224,370,144,57,127,253,238,287,430,485,477,299,235,6,15,36,82,176,319,277,155,297,240,389,414,447,385,476,487,354,462,269,373,469,83,177,136,268,413,207,352,340,454,452,143,280,285,427,482,293,249,398,437,387,25,58,130,260,410,217,362,409,246,347,94,196,337,22,53,120,242,392,417,483,241,226,356,451,328,35,79,169,311,442,30,70,153,292,404,441,481,252,400,346,458,68,150,52,117,234,333,76,164,305,439,382,38,87,167,39,88,186,188,256,113,228,372,468,279,422,96,201,291,433,183,108,221,365,445,327,218,44,99,206,275,420,158,289,325,435,443,484,182,323,141,69,152,118,237,314,321,236,222,366,466,438,415,62,137,33,75,162,146,231,377,471,274,419,380,47,107,219,324,350,151,288,418,301,434,171,173,31,72,157,104,214,258,408,245,361,243,168,7,17,40,91,97,203,348,460,111,210,284,55,4,10,24,56,81,11,27,63,140,254,402,432,381,473,200,342,456,261,283,134,265,66,9,21,50,114,195,14,34,78,166,129,257,406,386,49,112,227,371,467,394,41,93,71,154,294,46,105,215,358,184,326,449,212,357,464,390,463,149,286,429,455,424,85,180,59,131,262,51,116,170,313,444,486,428,367,304,426,374,470,208,353,103,65,145,282,272,138,271,232,378,459,198,339,360,194,336,351,461,295,124,250,391,479,187,329,330,128,255,121,244,316,174,122,202,345,457,160,302,401,480,475,100,209,355,119,239,359,290,185,3,8,20,48,110,225,343,90,191,192,331,405,126,251,399,334,423,335,266,412,248,190,308,349,450,474,197,338,364,101,16,37,84,179,307,440,448,388,478,436,383,18,43,98,205,86,181,322,298,384,368,106,216,276,421,139,273,77,165,306,296,312,178,320,396,317,446,109,223,369,220,163,281,425,431,465,395,315,26,60,132,263,61,135,115,230,376,363,393,310,19,45,102,211,204,54,123,247,375,407,318,125,12,29,67,148,175,80,172,270,416,403,73,159,300,397,344,42,95,199,341,267,213,147,23)Polycyclic presentation:
3^3,487|a^3=b,b^3=c,d^a=d^362,d^b=d^232189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13149, 14);