Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14523747⋊C11 |
| Fitting, socle, derived, Sylow | C232 ⋊ C4×C11 |
| Hall | #19154120 ⋊ C4 |
| Hall | #14523747 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C232 | C4×C11 |
| prime radical | #26042787 | C2 |
| cosocle | C23⋊D23 | C2×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 46 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2)(3,16,36,12,43,41,13,31,9,25,42,17,7,34,44,29,40,5,32,4,22,27,8,18,20,30,39,26,33,14,23,10,37,6,21,19,28,35,46,15,45,11,38,24);(1,3,7,9,20,13,22,39,28,40,32,42,37,45,46,44,43,38,33,36,23,21,8)(2,16,34,25,30,31,27,26,35,5,4,17,6,11,15,29,41,24,14,12,10,19,18)Polycyclic presentation:
2,11,2,23^2|a^2=c,d^a=d^3e^21,e^a=d^5e^20,d^b=d^2,e^b=e^2,d^c=d^22,e^c=e^2256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 50);