Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | D3×(C2×AGL(1,𝔽5))⋊C4 |
| Fitting | C2×C3×C4×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C2×#95 |
| Sylow | C5 ⋊ D3×#95 |
| Sylow | C3 ⋊ C2×(C2×AGL(1,𝔽5))⋊C4 |
660 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64920, #14282694, D3×#64868, … |
| maximal normal subgroup of | D3×#64920, #14282694, D3×#64868, … |
| maximal quotient of | Dic3×(C2×AGL(1,𝔽5))⋊C4, #14279878, #14279881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6125);