Finite Group DatabasebetaFinite Group Databasebeta| order | 32460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C541⋊C5 |
| unambiguous semidirect product | C3⋊(C22×C541⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C541⋊C5) |
| unambiguous semidirect product | (C2×D3×C541)⋊C5 |
| Fitting, socle | C2×C3×C541 ⋊ C2×C5 |
| derived, Hall | C3×C541 ⋊ C22×C5 |
| Hall | C3×C541⋊C5 ⋊ C22 |
| Hall | C2×D3×C541 ⋊ C5 |
| Sylow | C541 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C22×C541⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C541⋊C5 |
| commutator, cosocle, hypocenter | C3×C541 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C541 | C2×C5 |
| LCS | G ▷ C3×C541 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3246 |
678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32460, 37);