Finite Group DatabasebetaFinite Group Databasebeta| order | 32460 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊(C541⋊C3) |
| unambiguous semidirect product | C22⋊(C5×C541⋊C3) |
| unambiguous semidirect product | (C22×C5)⋊(C541⋊C3) |
| unambiguous semidirect product | (C5×C541)⋊A4 |
| Fitting, socle, Hall | C22×C5×C541 ⋊ C3 |
| derived, Hall | C22×C541 ⋊ C3×C5 |
| Hall | C5×C541 ⋊ A4 |
| Sylow | C541 ⋊ C5×A4 |
| Hall | C22×C5 ⋊ C541⋊C3 |
| Sylow | C22 ⋊ C5×C541⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊(C541⋊C3) |
| commutator, cosocle, hypocenter | C22×C541 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C541 | C3 |
| LCS | G ▷ C22×C541 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10820 |
3620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32460, 62);