Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65758 |
| Hall | C3×C5 ⋊ #423 |
| Sylow | C5 ⋊ C3×#423 |
252 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 116 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)(14,17)(18,20);(9,10,11,12);(5,6,7,8)(10,12)(13,14,15,18,16,17,19,20)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598508, #14276976, C3×#10598772, … |
| maximal normal subgroup of | C3×#10598508, #14276976, C3×#10598772, … |
| maximal quotient of | C3×#10604696, C3×#10604697, C3×#10604698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6486);