Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D1233 |
| unambiguous semidirect product | C9⋊(C13×D137) |
| unambiguous semidirect product | C137⋊(C13×D9) |
| Fitting, Hall | C9×C13×C137 ⋊ C2 |
| derived, Hall | C9×C137 ⋊ C2×C13 |
| Hall | C13×C137 ⋊ D9 |
| Sylow | C137 ⋊ C13×D9 |
| Hall | C9×C13 ⋊ D137 |
| Sylow | C9 ⋊ C13×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D1233 |
| commutator, cosocle, hypocenter | C9×C137 | C2×C13 |
| Frattini | C3 | C13×D411 |
| Fitting | C9×C13×C137 | C2 |
| socle | C3×C13×C137 | D3 |
| LCS | G ▷ C9×C137 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16029 |
8034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 7);