Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D49×#66526 |
| Fitting, derived, Hall | C37×C49 ⋊ C2×C9 |
| Hall | C49×#66526 ⋊ C2 |
| Hall | C37×D49 ⋊ C9 |
| Sylow | C49 ⋊ C2×#66526 |
| Sylow | C37 ⋊ C9×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C37×C49 | C2×C9 |
| Frattini | C7 | D7×#66526 |
| socle | C7×C37 | C9×D7 |
| prime radical | D49×C37⋊C3 | C3 |
| cosocle | C49×C37⋊C3 | C2×C3 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 37);