Finite Group DatabasebetaFinite Group Databasebeta| order | 24825 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C331 ⋊ C3×C5 |
| derived, Sylow | C331 ⋊ C3×C52 |
| Hall | C5×C331⋊C5 ⋊ C3 |
| Hall | C331⋊C3 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C331⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C331 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C331 | C3×C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1655 |
185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24825, 6);