Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65061 |
| Fitting | C3×C5×#102 ⋊ C2 |
| Hall | C3×C5 ⋊ #416 |
| Sylow | C5 ⋊ C3×#416 |
316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(13,15,16,24,18,25,17,23)(14,20,21,27,19,26,22,28);(14,19)(15,23)(16,17)(20,27)(24,25)(26,28);(5,6)(7,8)(13,14)(15,20)(16,21)(17,22)(18,19)(23,28)(24,27)(25,26)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603959, #14295926, C3×#10603960, … |
| maximal normal subgroup of | C3×#10603959, #14295926, C3×#10603960, … |
| maximal quotient of | C3×#10598958, C3×#10598962, C3×#10598966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3864);