Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| direct product | C22×D3×C24⋊C5 |
| unambiguous semidirect product | C3⋊(C23×C24⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C24⋊C5) |
| unambiguous semidirect product | (C26×D3)⋊C5 |
| Fitting, socle | C26×C3 ⋊ C2×C5 |
| derived | C24×C3 ⋊ C23×C5 |
| Hall | C26×D3 ⋊ C5 |
| Sylow | C3 ⋊ C23×C24⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C24⋊C5 |
| commutator, cosocle, hypocenter | C24×C3 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C26×C3 | C2×C5 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C22 | |
11800 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 11800 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240410);