Finite Group DatabasebetaFinite Group Databasebeta| order | 23134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11567 |
| unambiguous semidirect product | C43⋊D269 |
| unambiguous semidirect product | C269⋊D43 |
| Fitting, socle, derived, Hall | C43×C269 ⋊ C2 |
| Sylow | C269 ⋊ D43 |
| Sylow | C43 ⋊ D269 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C269 | C2 |
| LCS | G ▷ C43×C269 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 312 |
| transitive degree | μt(G) = 11567 |
A minimal faithful permutation representation — 2 generators on 312 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);(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(45,312)(46,311)(47,310)(48,309)(49,308)(50,307)(51,306)(52,305)(53,304)(54,303)(55,302)(56,301)(57,300)(58,299)(59,298)(60,297)(61,296)(62,295)(63,294)(64,293)(65,292)(66,291)(67,290)(68,289)(69,288)(70,287)(71,286)(72,285)(73,284)(74,283)(75,282)(76,281)(77,280)(78,279)(79,278)(80,277)(81,276)(82,275)(83,274)(84,273)(85,272)(86,271)(87,270)(88,269)(89,268)(90,267)(91,266)(92,265)(93,264)(94,263)(95,262)(96,261)(97,260)(98,259)(99,258)(100,257)(101,256)(102,255)(103,254)(104,253)(105,252)(106,251)(107,250)(108,249)(109,248)(110,247)(111,246)(112,245)(113,244)(114,243)(115,242)(116,241)(117,240)(118,239)(119,238)(120,237)(121,236)(122,235)(123,234)(124,233)(125,232)(126,231)(127,230)(128,229)(129,228)(130,227)(131,226)(132,225)(133,224)(134,223)(135,222)(136,221)(137,220)(138,219)(139,218)(140,217)(141,216)(142,215)(143,214)(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)Polycyclic presentation:
2,43,269|b^a=b^42,c^a=c^2685785 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23134, 3);