Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#16813380⋊C3 |
| unambiguous semidirect product | #16813380⋊C32 |
| unambiguous semidirect product | (C3×#16813380)⋊C3 |
| Fitting, socle | C3×C192 ⋊ C3×D5 |
| derived, Hall | C192⋊C5 ⋊ C2×C32 |
| Hall | C3×#11762245⋊C5 ⋊ C2 |
| Hall | #16813380 ⋊ C32 |
| Hall | C3×#11762245 ⋊ D5 |
| Sylow | C192 ⋊ C32×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813380⋊C3 |
| commutator, cosocle, hypocenter | C192⋊C5 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C3×D5 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 84);