Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C137 · Schur multiplier (H2) = C3 |
| direct product | C137×C3⋊D39 |
| unambiguous semidirect product | C3⋊(D39×C137) |
| unambiguous semidirect product | C13⋊(C3⋊D3×C137) |
| Fitting, socle, Hall | C32×C13×C137 ⋊ C2 |
| derived, Hall | C32×C13 ⋊ C2×C137 |
| Hall | C13×C137 ⋊ C3⋊D3 |
| Hall | C32×C137 ⋊ D13 |
| Sylow | C13 ⋊ C3⋊D3×C137 |
| Sylow | C32 ⋊ D13×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | C3⋊D39 |
| commutator, cosocle, hypocenter | C32×C13 | C2×C137 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C137 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C137 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16029 |
8220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 31);