Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×#14524206⋊C5 |
| unambiguous semidirect product | ((C19⋊D19)⋊C5)⋊C32 |
| unambiguous semidirect product | (C3×#14524206)⋊C5 |
| unambiguous semidirect product | (C3×(C19⋊D19)⋊C5)⋊C3 |
| Fitting, socle | C3×C192 ⋊ C2×C3×C5 |
| derived, Sylow | C192 ⋊ C2×C32×C5 |
| Hall | C3×#11762245⋊C5 ⋊ C2 |
| Hall | C3×#14524206 ⋊ C5 |
| Hall | (C19⋊D19)⋊C5 ⋊ C32 |
| Hall | C3×#11762245 ⋊ C2×C5 |
| Hall | C192⋊C5 ⋊ C2×C32 |
| Hall | C19⋊D19 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14524206⋊C5 |
| commutator, cosocle, hypocenter | C192 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 85);