Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#65699 |
| Fitting | C3×C5×C22⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ #385 |
| Sylow | C5 ⋊ C3×#385 |
468 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 128 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)(10,12)(13,14,15,16);(9,10)(11,12);(5,6,7,8)(14,16)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603919, #14300350, C2×C3×#65699, … |
| maximal normal subgroup of | C3×#10603919, #14300350, C2×C3×#65699, … |
| maximal quotient of | C3×#10604252, C3×#10603801, C3×#10604254, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6427);