Finite Group DatabasebetaFinite Group Databasebeta| order | 23188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D187⋊D31 |
| unambiguous semidirect product | D341⋊D17 |
| unambiguous semidirect product | D527⋊D11 |
| Fitting, socle, derived, Hall | C11×C17×C31 ⋊ C22 |
| Hall | C17×C31 ⋊ C2×D11 |
| Hall | C11×C31 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ C2×D31 |
| Sylow | C31 ⋊ D11×D17 |
| Sylow | C17 ⋊ D11×D31 |
| Sylow | C11 ⋊ D17×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C17×C31 | C22 |
| LCS | G ▷ C11×C17×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5797 |
Polycyclic presentation:
2^2,11,17,31|d^a=d^16,e^a=e^30,c^b=c^10,d^b=d^161495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23188, 20);