Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C3⋊(#585⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(#585⋊C5) |
| unambiguous semidirect product | (C2×#5968)⋊C5 |
| Hall | C2×#5968 ⋊ C5 |
| Sylow | C3 ⋊ C2×#585⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C24⋊C5 |
| commutator, cosocle, hypocenter | C3×2−1+4 | C22×C5 |
| Frattini | C2 | C2×D3×C24⋊C5 |
| Fitting | C2×C3×2−1+4 | C2×C5 |
| socle | C22×C3 | C2×C24⋊C5 |
| LCS | G ▷ C3×2−1+4 | |
| UCS | C1 ◁ C22 | |
1238 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240279);