Finite Group DatabasebetaFinite Group Databasebeta| order | 32396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C89 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D7×C89 |
| unambiguous semidirect product | C7⋊(C22×C13×C89) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C13×C89) |
| Fitting, socle | C2×C7×C13×C89 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C13×C89 |
| Hall | C7×C13×C89 ⋊ C22 |
| Hall | C7×C89 ⋊ C22×C13 |
| Hall | C7×C13 ⋊ C22×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13×C89 | D7 |
| commutator, cosocle, hypocenter | C7 | C22×C13×C89 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C89 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C13×C89 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16198 |
11570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32396, 32);