Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65281 |
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #399 |
| Sylow | C5 ⋊ C3×#399 |
372 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,12)(14,16)(17,19,20,23)(18,22,21,24);(13,14,15,16)(18,21)(22,24);(5,6)(7,8)(9,10)(11,12)(14,16)(17,18)(19,22)(20,21)(23,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598717, #14278290, C3×#10601961, … |
| maximal normal subgroup of | C3×#10598717, #14278290, C3×#10601961, … |
| maximal quotient of | C3×#10602363, C3×#10600221, C3×#10602361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4084);