Finite Group DatabasebetaFinite Group Databasebeta| order | 23276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C11⋊#14523747 |
| Fitting, socle, derived, Hall | C11×C232 ⋊ C4 |
| Sylow | C232 ⋊ Dic11 |
| Sylow | C11 ⋊ #14523747 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C232 | C4 |
| prime radical, cosocle | C11×C23⋊D23 | C2 |
| LCS | G ▷ C11×C232 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 506 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2)(3,6,7,15)(4,9,10,21)(5,12,13,25)(8,18,19,27)(11,22,23,20)(14,28,29,41)(16,26,31,38)(17,33,34,40)(24,39,35,44)(30,37,32,42)(36,45,43,46)(48,49)(50,51)(52,53)(54,55)(56,57);(1,3,8,20,37,41,39,45,33,12,26,9,21,38,25,40,46,44,28,42,22,19,7)(2,17,43,15,5,35,27,16,14,23,4,32,30,10,11,29,31,18,24,13,6,36,34)(47,48,50,52,54,56,57,55,53,51,49)Polycyclic presentation:
2^2,11,23^2|a^2=b,c^a=c^10,d^a=d^11e^12,e^a=d^9e^12,d^b=d^22,e^b=e^221466 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23276, 87);