Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | D3×2−1+4⋊C5 |
| unambiguous semidirect product | C3⋊(C2×2−1+4⋊C5) |
| unambiguous semidirect product | (D3×2−1+4)⋊C5 |
| Fitting, derived | C3×2−1+4 ⋊ C2×C5 |
| Hall | D3×2−1+4 ⋊ C5 |
| Sylow | C3 ⋊ C2×2−1+4⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C3×2−1+4 | C2×C5 |
| socle | C2×C3 | C2×C24⋊C5 |
| LCS | G ▷ C3×2−1+4 | |
| UCS | C1 ◁ C2 | |
184 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#66243, #14514346, #14514347, … |
| maximal normal subgroup of | D3×#66243, #14514346, #14514347, … |
| maximal quotient of | C3⋊(#3531⋊C5), D3×#564⋊C5, Dic3×2−1+4⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11002);