Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#11725075 |
| derived, Sylow | C72 ⋊ C2×C9×C37 |
| Hall | C37×#89205 ⋊ C2 |
| Hall | C7×D7×C37 ⋊ C9 |
| Hall | C72×C37 ⋊ C2×C9 |
| Hall | #89205 ⋊ C2×C37 |
| Hall | C7×D7 ⋊ C9×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | #64422 |
| commutator, hypocenter | C72 | C2×C9×C37 |
| Frattini | C3 | C37×#64422 |
| Fitting, socle | C3×C72×C37 | C2×C3 |
| prime radical | C3×C7×D7×C37 | C3 |
| cosocle | C3×C72 | C2×C3×C37 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C37 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4662 |
1887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 114);