Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64856 |
| Hall | C3×C5 ⋊ #355 |
| Sylow | C5 ⋊ C3×#355 |
128 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6,8,7)(10,14,17,16)(11,18)(15,22,23,24)(19,20);(5,6,7,8)(9,10,11,15,13,17,18,23)(12,14,20,22,21,16,19,24)87 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598748, C3×#10598540, #14279407, … |
| maximal normal subgroup of | C3×#10598748, C3×#10598540, #14279407, … |
| maximal quotient of | C3×#10598686, C3×#10598688, C3×#10598499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 828);