Finite Group DatabasebetaFinite Group Databasebeta| order | 32025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#13046196⋊C5 |
| unambiguous semidirect product | #13046196⋊C52 |
| unambiguous semidirect product | (C5×#13046196)⋊C5 |
| Fitting, socle | C5×C7×C61 ⋊ C3×C5 |
| derived, Hall | C7×C61 ⋊ C3×C52 |
| Hall | C5×C7×C61⋊C5 ⋊ C3 |
| Hall | C5×C61⋊C5 ⋊ ΓL(1,𝔽8) |
| Hall | #13046196 ⋊ C52 |
| Sylow | C61 ⋊ C52×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C5×(C61⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13046196⋊C5 |
| commutator, cosocle, hypocenter | C7×C61 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C61 | C3×C5 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2135 |
265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32025, 13);