Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65784 |
| Fitting | C2×C3×C5×Q8 ⋊ C4 |
| Hall | C3×C5 ⋊ #421 |
| Sylow | C5 ⋊ C3×#421 |
308 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 96 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 — 3 generators on 24 points:
(1,2,3)(4,5,6,8,7)(9,12,14,21)(10,16,17,24)(11,18,13,20)(15,23,22,19);(9,11,14,13)(10,15,17,22)(12,20,21,18)(16,19,24,23);(5,6,7,8)(9,10,11,15,14,17,13,22)(12,19,18,16,21,23,20,24)96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10605012, #14297365, C3×#10604974, … |
| maximal normal subgroup of | C3×#10605012, #14297365, C3×#10604974, … |
| maximal quotient of | C3×#10604437, C3×#10604270, C3×#10604967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6512);