Finite Group DatabasebetaFinite Group Databasebeta| order | 13364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C257 ⋊ C4 |
| Sylow | C257 ⋊ #261 |
| Sylow | C13 ⋊ #11759967 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C257 | C4 |
| prime radical, cosocle | D3341 | C2 |
| LCS | G ▷ C13×C257 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 270 |
| transitive degree | μt(G) = 3341 |
A minimal faithful permutation representation — 2 generators on 270 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,151)(99,126,124,147)(103,128,129,143)(107,132,133,139)(111,136,137,135)(115,140,141,131)(119,144,145,127)(121,148,149,125)(130,155,156,174)(134,159,160,170)(138,163,164,166)(142,167,168,162)(146,171,172,158)(150,175,176,154)(152,157,178,153)(161,182,183,197)(165,186,187,193)(169,190,191,189)(173,194,195,185)(177,198,199,181)(179,184,201,180)(188,205,206,216)(192,209,210,212)(196,213,214,208)(200,217,218,204)(202,207,220,203)(211,224,225,231)(215,228,229,227)(219,232,233,223)(221,226,235,222)(230,239,240,242)(234,243,244,238)(236,241,246,237)(245,250,251,249)(247,252,253,248)(254,256,257,255)(259,260,261,263)(262,265,266,267)(264,269,270,268);(1,2,5,10,19,32,49,70,95,124,98,73,52,35,22,13,6,11,20,33,50,71,96,125,153,156,129,102,77,56,39,26,15,24,37,54,75,100,127,154,180,183,160,133,106,81,60,43,28,41,58,79,104,131,158,181,203,206,187,164,137,110,85,64,45,62,83,108,135,162,185,204,222,225,210,191,168,141,114,89,66,87,112,139,166,189,208,223,237,240,229,214,195,172,145,118,91,116,143,170,193,212,227,238,248,251,244,233,218,199,176,149,120,147,174,197,216,231,242,249,255,257,253,246,235,220,201,178,151,122,152,179,202,221,236,247,254,256,250,239,224,205,182,155,126,93,121,150,177,200,219,234,245,252,243,228,209,186,159,128,97,68,92,119,146,173,196,215,230,241,232,213,190,163,132,101,72,47,67,90,115,142,169,192,211,226,217,194,167,136,105,76,51,30,46,65,86,111,138,165,188,207,198,171,140,109,80,55,34,17,29,44,61,82,107,134,161,184,175,144,113,84,59,38,21,8,16,27,40,57,78,103,130,157,148,117,88,63,42,25,12,3,7,14,23,36,53,74,99,123,94,69,48,31,18,9,4)(258,259,262,267,269,260,264,270,263,268,265,266,261)Polycyclic presentation:
2^2,13,257|a^2=b,c^a=c^5,d^a=d^241,c^b=c^12,d^b=d^256839 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13364, 8);