Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C22 |
| direct product | A4×2−1+4⋊C5 |
| unambiguous semidirect product | C22⋊(C3×2−1+4⋊C5) |
| unambiguous semidirect product | (A4×2−1+4)⋊C5 |
| unambiguous semidirect product | (C22×2−1+4⋊C5)⋊C3 |
| Fitting, derived, Sylow | C22×2−1+4 ⋊ C3×C5 |
| Hall | C22×2−1+4⋊C5 ⋊ C3 |
| Hall | A4×2−1+4 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C22×2−1+4 | C3×C5 |
| socle | C23 | C3×C24⋊C5 |
| LCS | G ▷ C22×2−1+4 | |
| UCS | C1 ◁ C2 | |
275 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240058);