Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#65321 |
| Fitting | C3×C5×#120 ⋊ C2 |
| Hall | C3×C5 ⋊ B(4,𝔽2) |
| Sylow | C5 ⋊ C3×B(4,𝔽2) |
396 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 78 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)(4,5,7,8,6)(13,16);(9,11)(10,13)(12,15)(14,16);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602702, C3×#10599923, #14316648, … |
| maximal normal subgroup of | C3×#10602702, C3×#10599923, #14316648, … |
| maximal quotient of | C3×#10601761, C3×#10600489, C3×#10601769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4124);