Finite Group DatabasebetaFinite Group Databasebeta| order | 23718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11859 |
| unambiguous semidirect product | C3⋊D3953 |
| unambiguous semidirect product | C59⋊D201 |
| unambiguous semidirect product | C67⋊D177 |
| Fitting, socle, derived, Hall | C3×C59×C67 ⋊ C2 |
| Hall | C59×C67 ⋊ D3 |
| Hall | C3×C67 ⋊ D59 |
| Hall | C3×C59 ⋊ D67 |
| Sylow | C67 ⋊ D177 |
| Sylow | C59 ⋊ D201 |
| Sylow | C3 ⋊ D3953 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C59×C67 | C2 |
| LCS | G ▷ C3×C59×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 11859 |
A minimal faithful permutation representation — 2 generators on 129 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);(2,3)(5,62)(6,61)(7,60)(8,59)(9,58)(10,57)(11,56)(12,55)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(64,129)(65,128)(66,127)(67,126)(68,125)(69,124)(70,123)(71,122)(72,121)(73,120)(74,119)(75,118)(76,117)(77,116)(78,115)(79,114)(80,113)(81,112)(82,111)(83,110)(84,109)(85,108)(86,107)(87,106)(88,105)(89,104)(90,103)(91,102)(92,101)(93,100)(94,99)(95,98)(96,97)Polycyclic presentation:
2,3,59,67|b^a=b^2,c^a=c^58,d^a=d^665931 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23718, 9);