Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#30654579 |
| Fitting, socle, Hall | C2×C72×C37 ⋊ C9 |
| derived, Hall | C72×C37 ⋊ C2×C9 |
| Hall | C2×C72 ⋊ #66526 |
| Hall | C2×C37 ⋊ #89204 |
| Sylow | C72 ⋊ C2×#66526 |
| Sylow | C37 ⋊ C2×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30654579 |
| commutator, hypocenter | C72×C37 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C9 |
| prime radical | C2×C72×C37⋊C3 | C3 |
| cosocle | C72×C37⋊C3 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3626 |
506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 269);