Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65731 |
| Fitting | C3×C5×D8 ⋊ C4 |
| Hall | C3×C5 ⋊ #442 |
| Sylow | C5 ⋊ C3×#442 |
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3)(4,5,6,8,7)(10,13)(11,15)(14,16);(9,11)(10,14)(12,16)(13,15);(5,6,7,8)(9,10,12,13)(11,14,16,15)87 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10604125, C3×#10604124, C3×#10604133, … |
| maximal normal subgroup of | C3×#10604125, C3×#10604124, C3×#10604133, … |
| maximal quotient of | C3×#10603938, C3×#10604792, C3×#10604062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6459);