Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D3×D20 |
| Fitting | C22×C3×C4×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ C23×D4 |
| Sylow | C5 ⋊ C22×D3×D4 |
| Sylow | C3 ⋊ C23×D20 |
2724 conjugacy classes of subgroups; only the 648 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 648 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #14296853, #14296902, #14296992, … |
| maximal normal subgroup of | #14296853, #14296902, #14296992, … |
| maximal quotient of | C22×D3×#685, C22×D3×C4⋊Dic5, C2×C4×D3×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11209);