Finite Group DatabasebetaFinite Group Databasebeta| order | 32025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C61 · Schur multiplier (H2) = C5 |
| direct product | C61×C7⋊(C52⋊C3) |
| unambiguous semidirect product | C7⋊(C61×C52⋊C3) |
| unambiguous semidirect product | C52⋊(ΓL(1,𝔽8)×C61) |
| Fitting, socle, Hall | C52×C7×C61 ⋊ C3 |
| derived, Hall | C52×C7 ⋊ C3×C61 |
| Hall | C52×C61 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C61 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)×C61 |
| Sylow | C7 ⋊ C61×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C7⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C7 | C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C61 | C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6405 |
3721 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32025, 19);