Finite Group DatabasebetaFinite Group Databasebeta| order | 25818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C331 ⋊ C2×C3 |
| Hall | #27166532 ⋊ C2 |
| Hall | D4303 ⋊ C3 |
| Sylow | C331 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D331⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C331 | C2×C3 |
| LCS | G ▷ C13×C331 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 344 |
| transitive degree | μt(G) = 4303 |
A minimal faithful permutation representation — 2 generators on 344 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)(138,221,222,177,178,268)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,233,234,189,190,209)(156,240,241,196,197,204)(161,247,245,201,202,199)(165,252,238,206,207,193)(168,257,231,210,211,186)(179,273,274,224,225,314)(181,271,272,226,223,265)(184,217,270,228,229,266)(191,281,282,235,236,261)(198,288,289,242,243,256)(203,295,296,248,249,251)(208,301,293,253,254,246)(212,305,286,258,259,239)(215,308,279,262,263,232)(227,316,317,276,275,312)(230,269,315,278,277,313)(237,319,320,283,284,310)(244,323,324,290,291,307)(250,327,328,297,298,304)(255,331,330,302,303,300)(260,329,326,299,306,294)(264,325,322,292,309,287)(267,321,318,285,311,280)(333,337,338,334,335,339)(336,343,342,340,341,344);(1,2,5,11,19,32,51,74,103,138,179,225,275,284,291,298,303,306,309,311,313,314,278,228,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,227,277,178,223,236,243,249,254,259,263,266,268,312,318,279,231,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,237,285,229,137,176,190,197,202,207,211,214,216,265,310,322,286,238,192,151,112,68,28,43,44,27,42,63,89,120,156,198,244,292,262,183,102,135,149,155,160,164,167,169,213,261,307,326,293,245,195,147,97,47,66,82,67,46,65,92,124,161,203,250,299,258,210,142,73,100,114,119,123,126,128,166,209,256,304,330,296,241,188,132,70,95,117,111,96,69,94,127,165,208,255,302,253,206,163,107,50,71,84,88,91,93,125,162,204,251,300,328,289,234,173,99,130,158,153,146,131,98,129,168,212,260,297,248,201,159,122,78,31,48,59,62,64,90,121,157,199,246,294,324,282,220,134,171,205,200,194,187,172,133,170,215,264,290,242,196,154,118,87,55,18,29,39,41,61,86,116,152,193,239,287,320,272,175,218,257,252,247,240,233,219,174,217,267,283,235,189,148,113,83,58,36,10,16,24,38,57,81,110,145,186,232,280,317,222,270,308,305,301,295,288,281,271,221,269,276,226,180,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,184,230,274,315,321,325,329,331,327,323,319,316,273,224,177,136,101,72,49,30,17,9,3)(332,333,336,335,339,342,341,343,344,338,337,340,334)Polycyclic presentation:
2,3,13,331|c^a=c^12,d^a=d^330,c^b=c^3,d^b=d^299723 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25818, 23);