Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65695 |
| Hall | C3×C5 ⋊ #436 |
| Sylow | C5 ⋊ C3×#436 |
244 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,6,8,7)(9,10)(11,12)(14,19)(18,20);(9,10,11,12)(13,15,17,16)(14,18,19,20);(5,6,7,8)(9,10,11,12)(13,14,16,20,17,19,15,18)114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#65695, C3×D5⋊#436, D3×#65695, … |
| maximal normal subgroup of | C2×C3×#65695, C3×D5⋊#436, D3×#65695, … |
| maximal quotient of | C3×#10603947, C3×#10603979, C3×#10603948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6423);