Finite Group DatabasebetaFinite Group Databasebeta| order | 24414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C313 ⋊ C2×C3 |
| Hall | #27131943 ⋊ C2 |
| Hall | D4069 ⋊ C3 |
| Sylow | C313 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D313⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C313 | C2×C3 |
| LCS | G ▷ C13×C313 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 326 |
| transitive degree | μt(G) = 4069 |
A minimal faithful permutation representation — 2 generators on 326 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,263)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,232,233,189,190,209)(156,237,238,196,197,204)(161,242,240,201,202,199)(165,247,235,206,207,193)(168,252,230,210,211,186)(179,239,251,198,224,275)(181,266,267,225,223,260)(184,217,265,227,228,261)(191,268,272,226,234,256)(203,278,279,243,244,246)(208,281,276,248,249,241)(212,286,273,253,254,236)(215,290,270,257,258,231)(229,264,285,245,269,297)(250,304,302,282,283,280)(255,306,300,287,288,277)(259,307,298,291,292,274)(262,305,284,294,295,271)(289,311,312,299,296,303)(293,313,310,308,309,301)(315,319,320,316,317,321)(318,325,324,322,323,326);(1,2,5,11,19,32,51,74,103,138,179,196,154,118,87,55,18,29,39,41,61,86,116,152,193,236,274,299,287,253,210,142,73,100,114,119,123,126,128,166,209,251,285,305,307,306,304,269,178,223,234,239,244,249,254,258,261,263,272,220,134,171,205,200,194,187,172,133,170,215,259,293,310,300,276,240,195,147,97,47,66,82,67,46,65,92,124,161,203,245,227,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,226,189,148,113,83,58,36,10,16,24,38,57,81,110,145,186,231,271,282,248,206,163,107,50,71,84,88,91,93,125,162,204,246,280,303,313,311,294,228,137,176,190,197,202,207,211,214,216,260,267,175,218,252,247,242,237,232,219,174,217,262,296,309,312,302,279,238,188,132,70,95,117,111,96,69,94,127,165,208,250,284,270,230,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,225,180,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,184,229,243,201,159,122,78,31,48,59,62,64,90,121,157,199,241,277,301,308,291,257,183,102,135,149,155,160,164,167,169,213,256,222,265,290,286,281,278,224,268,266,221,264,283,288,292,295,297,275,233,173,99,130,158,153,146,131,98,129,168,212,255,289,298,273,235,192,151,112,68,28,43,44,27,42,63,89,120,156,198,177,136,101,72,49,30,17,9,3)(314,315,318,317,321,324,323,325,326,320,319,322,316)Polycyclic presentation:
2,3,13,313|c^a=c^12,d^a=d^312,c^b=c^3,d^b=d^214684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24414, 28);