Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14524212⋊C3 |
| unambiguous semidirect product | #14524212⋊(C3×C5) |
| unambiguous semidirect product | (C5×#14524212)⋊C3 |
| Fitting, socle, Hall | C5×C192 ⋊ C3×D3 |
| derived | #11762246 ⋊ C2×C3×C5 |
| Hall | C5×C19⋊C32 ⋊ C2 |
| Hall | C19⋊C32 ⋊ C2×C5 |
| Sylow | C192 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14524212⋊C3 |
| commutator, cosocle, hypocenter | #11762246 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C3×D3 |
| LCS | G ▷ #11762246 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 90);