Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#64418⋊C3 |
| unambiguous semidirect product | #64418⋊(C3×C37) |
| Fitting, socle, Hall | C72×C37 ⋊ C3×D3 |
| derived | #3862 ⋊ C2×C3×C37 |
| Hall | ΓL(1,𝔽8)2×C37 ⋊ C2 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×C37 |
| Sylow | C72 ⋊ C3×D3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #64418⋊C3 |
| commutator, cosocle, hypocenter | #3862 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C3×D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C37 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 518 |
740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 164);