Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C232 ⋊ C4×C11 |
| Hall | #19154123 ⋊ C4 |
| Hall | C23×Dic23 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26042801 |
| commutator, hypocenter | C232 | C4×C11 |
| Fitting, socle, cosocle | C2×C232 | C2×C11 |
| prime radical | C2×#19154123 | C2 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 1012 |
A minimal faithful permutation representation — 2 generators on 50 points:
(1,2,3,4)(6,9,10,17,18,25,20,21,11,22,23,7,8,12,13,24,19,14,26,15,16,27)(29,30,32,36,39,31,34,35,40,46,41)(33,38,44,50,42,37,43,49,48,45,47);(5,6,8,11,10,14,16,24,13,19,21,27,23,26,25,17,18,22,20,12,15,9,7)(28,29,31,35,41,47,30,33,39,36,42,48,34,32,37,43,46,50,40,38,45,49,44)Polycyclic presentation:
2,11,23^2,2|a^2=e,c^a=c^22,c^b=c^2,d^b=d^698 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 30);