Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C7 |
| direct product | C2×C37×#89205 |
| derived, Sylow | C72 ⋊ C2×C9×C37 |
| Hall | C2×C72×C37 ⋊ C9 |
| Hall | C72×C37 ⋊ C2×C9 |
| Hall | C2×C72 ⋊ C9×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C37 | #3862 |
| commutator, hypocenter | C72 | C2×C9×C37 |
| Frattini | C3 | C2×C37×#3862 |
| Fitting, socle, prime radical | C2×C3×C72×C37 | C3 |
| cosocle | C3×C72 | C2×C3×C37 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C3×C37 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4662 |
4218 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 142);