Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C19 |
| direct product | C3×D3×C192⋊C5 |
| unambiguous semidirect product | C3⋊(C2×C3×C192⋊C5) |
| unambiguous semidirect product | (C3×D3×C192)⋊C5 |
| Fitting, socle, Hall | C32×C192 ⋊ C2×C5 |
| derived | C3×C192 ⋊ C2×C3×C5 |
| Hall | C32×C192⋊C5 ⋊ C2 |
| Hall | C3×D3×C192 ⋊ C5 |
| Sylow | C192 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ C2×C192⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C192⋊C5 |
| commutator, cosocle, hypocenter | C3×C192 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C192 | C2×C5 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
693 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 146);