Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D37×C49⋊C3 |
| Fitting | C3×C37×C49 ⋊ C2×C3 |
| derived, Hall | C37×C49 ⋊ C2×C32 |
| Hall | C3×C37×C49⋊C3 ⋊ C2 |
| Hall | C49×D37 ⋊ C32 |
| Sylow | C49 ⋊ C32×D37 |
| Sylow | C37 ⋊ C2×C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D37×C49⋊C3 |
| commutator, cosocle, hypocenter | C37×C49 | C2×C32 |
| Frattini | C7 | C3×ΓL(1,𝔽8)×D37 |
| Fitting | C3×C37×C49 | C2×C3 |
| socle | C3×C7×C37 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 51);