Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D259 |
| derived, Hall | C72×C37 ⋊ C2×C9 |
| Hall | C7×C37×C7⋊C9 ⋊ C2 |
| Hall | C7×D259 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ D37 |
| Sylow | C72 ⋊ C9×D37 |
| Sylow | C37 ⋊ D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D259 |
| commutator, hypocenter | C72×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C37 | C2×C3 |
| prime radical | C3×C7×D259 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4662 |
1965 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 136);