Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #19154125 ⋊ C4 |
| Sylow | C232 ⋊ Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26042805 |
| commutator, hypocenter | #19154125 | C4 |
| Fitting, socle | C2×C232 | D11 |
| prime radical, cosocle | C2×#19154125 | C2 |
| LCS | G ▷ #19154125 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 92 |
A minimal faithful permutation representation — 2 generators on 50 points:
(1,7,24,29,31,30,19,21,23,2,3,15,40,45,22,32,33,35,39,4,6,28,5,36,37,42,41,44,34,8,10,9,11,46,25,27,38,26,13,16,18,17,20,14,12,43)(47,48,49,50);(3,5,10,6,12,22,18,20,34,25,13)(4,7,14,26,30,29,36,21,8,16,9)(11,19,31,39,40,23,38,37,33,41,24)(15,27,42,46,43,35,28,44,45,32,17)Polycyclic presentation:
2,11,23^2,2|a^2=e,b^a=b^10,c^a=d,d^a=c,c^b=c^16,d^b=d^13128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 34);