Finite Group DatabasebetaFinite Group Databasebeta| order | 24806 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12403 |
| unambiguous semidirect product | C79⋊D157 |
| unambiguous semidirect product | C157⋊D79 |
| Fitting, socle, derived, Hall | C79×C157 ⋊ C2 |
| Sylow | C157 ⋊ D79 |
| Sylow | C79 ⋊ D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C79×C157 | C2 |
| LCS | G ▷ C79×C157 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 236 |
| transitive degree | μt(G) = 12403 |
A minimal faithful permutation representation — 2 generators on 236 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);(2,79)(3,78)(4,77)(5,76)(6,75)(7,74)(8,73)(9,72)(10,71)(11,70)(12,69)(13,68)(14,67)(15,66)(16,65)(17,64)(18,63)(19,62)(20,61)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(81,236)(82,235)(83,234)(84,233)(85,232)(86,231)(87,230)(88,229)(89,228)(90,227)(91,226)(92,225)(93,224)(94,223)(95,222)(96,221)(97,220)(98,219)(99,218)(100,217)(101,216)(102,215)(103,214)(104,213)(105,212)(106,211)(107,210)(108,209)(109,208)(110,207)(111,206)(112,205)(113,204)(114,203)(115,202)(116,201)(117,200)(118,199)(119,198)(120,197)(121,196)(122,195)(123,194)(124,193)(125,192)(126,191)(127,190)(128,189)(129,188)(130,187)(131,186)(132,185)(133,184)(134,183)(135,182)(136,181)(137,180)(138,179)(139,178)(140,177)(141,176)(142,175)(143,174)(144,173)(145,172)(146,171)(147,170)(148,169)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)Polycyclic presentation:
2,79,157|b^a=b^78,c^a=c^1566203 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24806, 3);