Finite Group DatabasebetaFinite Group Databasebeta| order | 23014 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11507 |
| unambiguous semidirect product | C37⋊D311 |
| unambiguous semidirect product | C311⋊D37 |
| Fitting, socle, derived, Hall | C37×C311 ⋊ C2 |
| Sylow | C311 ⋊ D37 |
| Sylow | C37 ⋊ D311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C311 | C2 |
| LCS | G ▷ C37×C311 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 348 |
| transitive degree | μt(G) = 11507 |
A minimal faithful permutation representation — 2 generators on 348 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348);(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(39,348)(40,347)(41,346)(42,345)(43,344)(44,343)(45,342)(46,341)(47,340)(48,339)(49,338)(50,337)(51,336)(52,335)(53,334)(54,333)(55,332)(56,331)(57,330)(58,329)(59,328)(60,327)(61,326)(62,325)(63,324)(64,323)(65,322)(66,321)(67,320)(68,319)(69,318)(70,317)(71,316)(72,315)(73,314)(74,313)(75,312)(76,311)(77,310)(78,309)(79,308)(80,307)(81,306)(82,305)(83,304)(84,303)(85,302)(86,301)(87,300)(88,299)(89,298)(90,297)(91,296)(92,295)(93,294)(94,293)(95,292)(96,291)(97,290)(98,289)(99,288)(100,287)(101,286)(102,285)(103,284)(104,283)(105,282)(106,281)(107,280)(108,279)(109,278)(110,277)(111,276)(112,275)(113,274)(114,273)(115,272)(116,271)(117,270)(118,269)(119,268)(120,267)(121,266)(122,265)(123,264)(124,263)(125,262)(126,261)(127,260)(128,259)(129,258)(130,257)(131,256)(132,255)(133,254)(134,253)(135,252)(136,251)(137,250)(138,249)(139,248)(140,247)(141,246)(142,245)(143,244)(144,243)(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)(152,235)(153,234)(154,233)(155,232)(156,231)(157,230)(158,229)(159,228)(160,227)(161,226)(162,225)(163,224)(164,223)(165,222)(166,221)(167,220)(168,219)(169,218)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,211)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,204)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,197)(191,196)(192,195)(193,194)Polycyclic presentation:
2,37,311|b^a=b^36,c^a=c^3105755 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23014, 3);