Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#65765 |
| Fitting | C22×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #380 |
| Sylow | C5 ⋊ C3×#380 |
468 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 140 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) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3)(4,5,6,8,7)(10,12);(13,14,15,16);(5,6,7,8)(9,10)(11,12)(14,16)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598506, C3×#10598764, #14277049, … |
| maximal normal subgroup of | C3×#10598506, C3×#10598764, #14277049, … |
| maximal quotient of | C3×#10604909, C3×#10604197, C3×#10604198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6493);