Finite Group DatabasebetaFinite Group Databasebeta| order | 23364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C11⋊(C59⋊#157) |
| unambiguous semidirect product | C59⋊(C11⋊#157) |
| Fitting, socle, derived, Hall | C32×C11×C59 ⋊ C4 |
| Hall | C11×C59 ⋊ #157 |
| Hall | C32×C59 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic59 |
| Sylow | C59 ⋊ C11⋊#157 |
| Sylow | C11 ⋊ C59⋊#157 |
| Sylow | C32 ⋊ Dic649 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C59 | C4 |
| prime radical, cosocle | C11×C3⋊D3×C59 | C2 |
| LCS | G ▷ C32×C11×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3894 |
Polycyclic presentation:
2^2,3^2,11,59|a^2=b,c^a=cd,d^a=cd^2,e^a=e^10,f^a=f^58,c^b=c^2,d^b=d^21950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23364, 41);