Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D187⋊D33 |
| Fitting, socle, derived, Hall | C3×C112×C17 ⋊ C22 |
| Hall | C112×C17 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D17 |
| Sylow | C112 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ D112 |
| Sylow | C17 ⋊ D11×D33 |
| Sylow | C3 ⋊ (C11⋊D11)⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112×C17 | C22 |
| LCS | G ▷ C3×C112×C17 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1122 |
Polycyclic presentation:
2^2,3,11^2,17|d^a=d^10,f^a=f^16,c^b=c^2,d^b=d^10,e^b=e^101590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 92);