Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C11⋊(C23⋊Dic23) |
| unambiguous semidirect product | C23⋊Dic253 |
| derived, Hall | C11×C232 ⋊ C4 |
| Sylow | C232 ⋊ Dic11 |
| Sylow | C11 ⋊ C23⋊Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C23⋊D23) |
| commutator, hypocenter | C11×C232 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C232 | C2 |
| LCS | G ▷ C11×C232 | |
| UCS | C1 ◁ C2 | |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 23276 |
A minimal faithful permutation representation — 3 generators on 61 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61);(1,2,4,6,8,10,11,9,7,5,3)(39,40,42,44,46,48,50,52,54,56,58,60,61,59,57,55,53,51,49,47,45,43,41);(16,17,19,21,23,25,27,29,31,33,35,37,38,36,34,32,30,28,26,24,22,20,18)Polycyclic presentation:
2,11,23^2,2|a^2=e,b^a=b^10,c^a=c^22,d^a=d^225822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 42);