Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26042791⋊C2 |
| unambiguous semidirect product | #26042797⋊C2 |
| unambiguous semidirect product | #26042801⋊C2 |
| Fitting, socle, derived, Sylow | C232 ⋊ C22×C11 |
| Hall | #19154123 ⋊ C22 |
| Hall | D232 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232 | C22×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 506 |
A minimal faithful permutation representation — 2 generators on 46 points:
(2,5,6,13,14,21,16,17,7,18,19,3,4,8,9,20,15,10,22,11,12,23)(24,25,31,26,36,32,45,27,38,34,39)(28,40,35,44,42,29,30,46,37,43,33);(1,2,4,7,6,10,12,20,9,15,17,23,19,22,21,13,14,18,16,8,11,5,3)(25,26)(27,29)(28,32)(30,35)(31,38)(33,39)(34,41)(36,44)(37,43)(40,42)(45,46)Polycyclic presentation:
2^2,11,23^2|e^a=e^22,d^b=d^22,d^c=d^2,e^c=e^959 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 55);