Finite Group DatabasebetaFinite Group Databasebeta| order | 24825 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C331⋊C3 |
| Fitting, socle, Hall | C52×C331 ⋊ C3 |
| derived, Sylow | C331 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C331⋊C3 |
| commutator, cosocle, hypocenter | C331 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C331 | C3 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8275 |
2825 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24825, 10);