Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D855 |
| unambiguous semidirect product | C5⋊(C19×D171) |
| unambiguous semidirect product | C9⋊(C19×D95) |
| unambiguous semidirect product | C19⋊(C19×D45) |
| Fitting, Hall | C5×C9×C192 ⋊ C2 |
| derived | C5×C9×C19 ⋊ C2×C19 |
| Hall | C9×C192 ⋊ D5 |
| Hall | C5×C192 ⋊ D9 |
| Sylow | C192 ⋊ D45 |
| Hall | C5×C9 ⋊ C19×D19 |
| Sylow | C9 ⋊ C19×D95 |
| Sylow | C5 ⋊ C19×D171 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D855 |
| commutator, cosocle, hypocenter | C5×C9×C19 | C2×C19 |
| Frattini | C3 | C19×D285 |
| Fitting | C5×C9×C192 | C2 |
| socle | C3×C5×C192 | D3 |
| LCS | G ▷ C5×C9×C19 | |
| UCS | C1 ◁ C19 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
8151 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 70);