Finite Group DatabasebetaFinite Group Databasebeta| order | 22922 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11461 |
| unambiguous semidirect product | C73⋊D157 |
| unambiguous semidirect product | C157⋊D73 |
| Fitting, socle, derived, Hall | C73×C157 ⋊ C2 |
| Sylow | C157 ⋊ D73 |
| Sylow | C73 ⋊ D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73×C157 | C2 |
| LCS | G ▷ C73×C157 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 230 |
| transitive degree | μt(G) = 11461 |
A minimal faithful permutation representation — 2 generators on 230 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);(2,73)(3,72)(4,71)(5,70)(6,69)(7,68)(8,67)(9,66)(10,65)(11,64)(12,63)(13,62)(14,61)(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(75,230)(76,229)(77,228)(78,227)(79,226)(80,225)(81,224)(82,223)(83,222)(84,221)(85,220)(86,219)(87,218)(88,217)(89,216)(90,215)(91,214)(92,213)(93,212)(94,211)(95,210)(96,209)(97,208)(98,207)(99,206)(100,205)(101,204)(102,203)(103,202)(104,201)(105,200)(106,199)(107,198)(108,197)(109,196)(110,195)(111,194)(112,193)(113,192)(114,191)(115,190)(116,189)(117,188)(118,187)(119,186)(120,185)(121,184)(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)(141,164)(142,163)(143,162)(144,161)(145,160)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)Polycyclic presentation:
2,73,157|b^a=b^72,c^a=c^1565732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22922, 3);