Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C49⋊C3×D111 |
| unambiguous semidirect product | C3⋊(D37×C49⋊C3) |
| Fitting, derived | C3×C37×C49 ⋊ C2×C3 |
| Hall | C3×C37×C49⋊C3 ⋊ C2 |
| Hall | C37×C49 ⋊ C3×D3 |
| Hall | C3×C49⋊C3 ⋊ D37 |
| Sylow | C49 ⋊ C3×D111 |
| Sylow | C37 ⋊ D3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C37×C49 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×D111 |
| socle | C3×C7×C37 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C3×C37×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
1083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 67);