Finite Group DatabasebetaFinite Group Databasebeta| order | 32487 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C17×#63270 |
| Fitting, socle, Hall | C72×C13×C17 ⋊ C3 |
| derived | C7×C13 ⋊ C3×C7×C17 |
| Hall | C72×C17 ⋊ C13⋊C3 |
| Hall | C72×C13 ⋊ C3×C17 |
| Hall | C13×C17 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C17×C13⋊C3 |
| Sylow | C13 ⋊ C7×C17×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | #63270 |
| commutator, cosocle, hypocenter | C7×C13 | C3×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13×C17 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C7×C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4641 |
3927 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32487, 9);