Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×#65780 |
| Fitting | C2×C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #390 |
| Sylow | C5 ⋊ C3×#390 |
516 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 516 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) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3)(4,5,6,8,7)(10,12)(14,16);(13,14,15,16);(5,6,7,8)(9,10)(11,12)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598568, #14279126, C3×#10605015, … |
| maximal normal subgroup of | C3×#10598568, #14279126, C3×#10605015, … |
| maximal quotient of | C3×#10604342, C3×#10604253, C3×#10604954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6508);