Finite Group DatabasebetaFinite Group Databasebeta| order | 32325 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C3×C5×C431 ⋊ C5 |
| derived, Sylow | C431 ⋊ C3×C52 |
| Hall | C3×C431 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C431⋊C5 |
| commutator, cosocle, hypocenter | C431 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C431 | C5 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6465 |
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32325, 4);