Finite Group DatabasebetaFinite Group Databasebeta| order | 23452 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D143⋊D41 |
| unambiguous semidirect product | D451⋊D13 |
| unambiguous semidirect product | D533⋊D11 |
| Fitting, socle, derived, Hall | C11×C13×C41 ⋊ C22 |
| Hall | C13×C41 ⋊ C2×D11 |
| Hall | C11×C41 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D41 |
| Sylow | C41 ⋊ D11×D13 |
| Sylow | C13 ⋊ D11×D41 |
| Sylow | C11 ⋊ D13×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C41 | C22 |
| LCS | G ▷ C11×C13×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5863 |
Polycyclic presentation:
2^2,11,13,41|d^a=d^12,e^a=e^40,c^b=c^10,d^b=d^121516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23452, 28);