Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | #3861×D37⋊C3 |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×#3861) |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C32 |
| Hall | C37⋊C3×#3861 ⋊ C2 |
| Hall | C72×D37 ⋊ C32 |
| Hall | D37 ⋊ C3×#3861 |
| Sylow | C72 ⋊ C3×D37⋊C3 |
| Sylow | C37 ⋊ C2×C3×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C2×C32 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 232);