Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D3×#564⋊C5 |
| unambiguous semidirect product | C3⋊(C2×#564⋊C5) |
| unambiguous semidirect product | (D3×#564)⋊C5 |
| Fitting, derived | C3×#564 ⋊ C2×C5 |
| Hall | D3×#564 ⋊ C5 |
| Sylow | C3 ⋊ C2×#564⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C3×#564 | C2×C5 |
| socle | C22×C3 | C2×C24⋊C5 |
| LCS | G ▷ C3×#564 | |
| UCS | C1 ◁ C22 | |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239378);