Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×#66297 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×#66297 |
| unambiguous semidirect product | (C3×#66297)⋊C2 |
| unambiguous semidirect product | (C3⋊#66297)⋊C2 |
| Fitting, socle | C24×C3 ⋊ C2×AGL(1,𝔽5) |
| derived | C3×C24⋊C5 ⋊ C2×C4 |
| Sylow | C3 ⋊ C2×#66297 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C24⋊C5 | C2×C4 |
| Fitting, socle | C24×C3 | C2×AGL(1,𝔽5) |
| prime radical | D3×(C24⋊C5)⋊C2 | C2 |
| cosocle | C3×(C24⋊C5)⋊C2 | C22 |
| LCS | G ▷ C3×C24⋊C5 | |
| UCS | C1 | |
322 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 30 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΣL(2,𝔽4), D3×AΓL(1,𝔽16), D3×#11757163⋊C2, … |
| maximal normal subgroup of | C2×D3×#66297 |
| maximal quotient of | C2×D3×#66297 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240390);