Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#20266606 |
| Fitting, socle, Hall | C5×C192 ⋊ C2×C9 |
| derived, Sylow | C192 ⋊ C2×C5×C9 |
| Hall | C5×#15692435 ⋊ C2 |
| Hall | C5×C19×D19 ⋊ C9 |
| Hall | #15692435 ⋊ C2×C5 |
| Hall | C19×D19 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20266606 |
| commutator, hypocenter | C192 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C2×C9 |
| prime radical | C5×#14524209 | C3 |
| cosocle | #11762246 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 109);