Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C37 · Schur multiplier (H2) = C3 |
| direct product | C2×ΓL(1,𝔽8)2×C37 |
| unambiguous semidirect product | (C2×C7×ΓL(1,𝔽8))⋊(C3×C37) |
| unambiguous semidirect product | (C2×#3861)⋊(C3×C37) |
| unambiguous semidirect product | (C2×#3862)⋊(C3×C37) |
| Fitting, socle, Hall | C2×C72×C37 ⋊ C32 |
| derived, Sylow | C72 ⋊ C2×C32×C37 |
| Hall | C72×C37 ⋊ C2×C32 |
| Hall | C2×C72 ⋊ C32×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | ΓL(1,𝔽8)2 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C37 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 263);