Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C37⋊#64418 |
| Fitting, socle | C3×C72×C37 ⋊ D3 |
| derived | C37×#3862 ⋊ C2×C3 |
| Hall | C3×C37×#3862 ⋊ C2 |
| Hall | C72×C37 ⋊ C3×D3 |
| Hall | C3×#3862 ⋊ D37 |
| Sylow | C72 ⋊ C3×D111 |
| Sylow | C37 ⋊ C3×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C37⋊#64418 |
| commutator, cosocle, hypocenter | C37×#3862 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C37 | D3 |
| LCS | G ▷ C37×#3862 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
1086 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 275);