Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| direct product | Dic3×2−1+4⋊C5 |
| unambiguous semidirect product | C3⋊(C4×2−1+4⋊C5) |
| unambiguous semidirect product | (Dic3×2−1+4)⋊C5 |
| derived | C3×2−1+4 ⋊ C4×C5 |
| Hall | Dic3×2−1+4 ⋊ C5 |
| Sylow | C3 ⋊ C4×2−1+4⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C24⋊C5 |
| commutator, hypocenter | C3×2−1+4 | C4×C5 |
| Fitting, cosocle | C2×C3×2−1+4 | C2×C5 |
| socle | C22×C3 | C2×C24⋊C5 |
| prime radical | C2×C3×2−1+4⋊C5 | C2 |
| LCS | G ▷ C3×2−1+4 | |
| UCS | C1 ◁ C22 | |
338 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 23 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, 239380);