Finite Group DatabasebetaFinite Group Databasebeta| order | 23182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11591 |
| unambiguous semidirect product | C67⋊D173 |
| unambiguous semidirect product | C173⋊D67 |
| Fitting, socle, derived, Hall | C67×C173 ⋊ C2 |
| Sylow | C173 ⋊ D67 |
| Sylow | C67 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C67×C173 | C2 |
| LCS | G ▷ C67×C173 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 240 |
| transitive degree | μt(G) = 11591 |
A minimal faithful permutation representation — 2 generators on 240 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);(2,67)(3,66)(4,65)(5,64)(6,63)(7,62)(8,61)(9,60)(10,59)(11,58)(12,57)(13,56)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(69,240)(70,239)(71,238)(72,237)(73,236)(74,235)(75,234)(76,233)(77,232)(78,231)(79,230)(80,229)(81,228)(82,227)(83,226)(84,225)(85,224)(86,223)(87,222)(88,221)(89,220)(90,219)(91,218)(92,217)(93,216)(94,215)(95,214)(96,213)(97,212)(98,211)(99,210)(100,209)(101,208)(102,207)(103,206)(104,205)(105,204)(106,203)(107,202)(108,201)(109,200)(110,199)(111,198)(112,197)(113,196)(114,195)(115,194)(116,193)(117,192)(118,191)(119,190)(120,189)(121,188)(122,187)(123,186)(124,185)(125,184)(126,183)(127,182)(128,181)(129,180)(130,179)(131,178)(132,177)(133,176)(134,175)(135,174)(136,173)(137,172)(138,171)(139,170)(140,169)(141,168)(142,167)(143,166)(144,165)(145,164)(146,163)(147,162)(148,161)(149,160)(150,159)(151,158)(152,157)(153,156)(154,155)Polycyclic presentation:
2,67,173|b^a=b^66,c^a=c^1725797 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23182, 3);