Finite Group DatabasebetaFinite Group Databasebeta| order | 32058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C137 · Schur multiplier (H2) = C1 |
| direct product | D3×C13⋊C3×C137 |
| unambiguous semidirect product | C3⋊(C2×C13⋊C3×C137) |
| unambiguous semidirect product | (D3×C13)⋊(C3×C137) |
| unambiguous semidirect product | (D3×C13×C137)⋊C3 |
| Fitting, socle | C3×C13×C137 ⋊ C2×C3 |
| derived | C3×C13 ⋊ C2×C3×C137 |
| Hall | C3×C13⋊C3×C137 ⋊ C2 |
| Hall | C13×C137 ⋊ C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×C137 |
| Sylow | C13 ⋊ C3×D3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D3×C13⋊C3 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C137 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C137 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5343 |
2877 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32058, 19);