Finite Group DatabasebetaFinite Group Databasebeta| order | 24915 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22552176⋊C3 |
| Fitting, socle, derived, Hall | C11×C151 ⋊ C3×C5 |
| Hall | #22552176 ⋊ C3 |
| Hall | C11×C151⋊C3 ⋊ C5 |
| Hall | C151⋊C3 ⋊ C11⋊C5 |
| Sylow | C151 ⋊ C3×C11⋊C5 |
| Sylow | C11 ⋊ (C151⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C151 | C3×C5 |
| LCS | G ▷ C11×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1661 |
Polycyclic presentation:
3,5,11,151|d^a=d^32,c^b=c^4,d^b=d^8131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24915, 12);