Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#66258 |
| Fitting | C2×C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #518 |
| Sylow | C5 ⋊ C3×#518 |
676 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 276 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 — 4 generators on 16 points:
(1,2,3)(4,5,6,8,7)(10,14)(13,16);(11,15)(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×#10603925, #14299608, C3×#10603919, … |
| maximal normal subgroup of | C3×#10603925, #14299608, C3×#10603919, … |
| maximal quotient of | C3×#10617067, C3×#10617098, C3×#10617172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11161);