Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C192 · Schur multiplier (H2) = C3×C19 |
| direct product | C192×C3⋊D15 |
| unambiguous semidirect product | C3⋊(C192×D15) |
| unambiguous semidirect product | C5⋊(C3⋊D3×C192) |
| Fitting, socle, Hall | C32×C5×C192 ⋊ C2 |
| derived, Hall | C32×C5 ⋊ C2×C192 |
| Hall | C32×C192 ⋊ D5 |
| Hall | C5×C192 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D5×C192 |
| Sylow | C5 ⋊ C3⋊D3×C192 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C192 | C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C5 | C2×C192 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C192 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C192 | |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
8664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 219);