Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1813 |
| Fitting, Hall | C9×C37×C49 ⋊ C2 |
| derived, Hall | C37×C49 ⋊ C2×C9 |
| Hall | C9×C49 ⋊ D37 |
| Hall | C9×C37 ⋊ D49 |
| Sylow | C49 ⋊ C9×D37 |
| Sylow | C37 ⋊ C9×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1813 |
| commutator, hypocenter | C37×C49 | C2×C9 |
| Frattini | C3×C7 | C3×D259 |
| Fitting | C9×C37×C49 | C2 |
| socle | C3×C7×C37 | C3×D7 |
| prime radical | C3×D1813 | C3 |
| cosocle | C3×C37×C49 | C2×C3 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16317 |
8172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 20);