Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C32 |
| Hall | C5×C19⋊C32 ⋊ C2 |
| Hall | C19×D95 ⋊ C32 |
| Hall | C19⋊C32 ⋊ D5 |
| Sylow | C192 ⋊ C32×D5 |
| Sylow | C5 ⋊ C19⋊C3×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C192 | C2×C32 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
108 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 570 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 124);