Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66085 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #577 |
| Sylow | C5 ⋊ C3×#577 |
516 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 214 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) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,17,13,18,19,23)(10,15,16,22,14,20,21,24);(10,14)(15,20)(16,21)(22,24);(9,10)(11,15)(12,16)(13,14)(17,22)(18,20)(19,21)(23,24);(5,6)(7,8)(11,17)(12,19)(15,22)(16,21)(18,23)(20,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612670, C3×#10611631, #14457704, … |
| maximal normal subgroup of | C3×#10612670, C3×#10611631, #14457704, … |
| maximal quotient of | C3×#10615528, C3×#10615537, C3×#10615515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9957);