Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic3×C24⋊C5 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C24⋊C5) |
| unambiguous semidirect product | (C25×Dic3)⋊C5 |
| derived | C24×C3 ⋊ C2×C4×C5 |
| Hall | C25×Dic3 ⋊ C5 |
| Sylow | C3 ⋊ C2×C4×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C24⋊C5 |
| commutator, hypocenter | C24×C3 | C2×C4×C5 |
| Frattini | C2 | C2×D3×C24⋊C5 |
| Fitting, socle | C26×C3 | C2×C5 |
| prime radical | C22×C3×C24⋊C5 | C2 |
| cosocle | C25×C3 | C22×C5 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C22 | |
2168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 2168 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240285);