Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#17987953 |
| Fitting, socle, Hall | C72×C37 ⋊ C2×C9 |
| derived | C7×C37 ⋊ C2×C7×C9 |
| Hall | C7×#14556423 ⋊ C2 |
| Hall | C7×D259 ⋊ C9 |
| Sylow | C72 ⋊ #66526⋊C2 |
| Sylow | C37 ⋊ C7×D7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #17987953 |
| commutator, hypocenter | C7×C37 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C2×C9 |
| prime radical | C7×(C37⋊C3)⋊D7 | C3 |
| cosocle | C7×C37⋊C3 | C2×C3×C7 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 175);