Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×#66068 |
| Fitting | C3×C5×C4⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #555 |
| Sylow | C5 ⋊ C3×#555 |
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(11,15)(13,16)(17,19,20,23)(18,21,22,24);(10,14)(11,15)(17,18,20,22)(19,24,23,21);(9,11,12,15)(10,13,14,16);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(19,23)(21,24)159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602058, C3×#10599284, #14289064, … |
| maximal normal subgroup of | C3×#10602058, C3×#10599284, #14289064, … |
| maximal quotient of | C3×#10607710, C3×#10606055, C3×#10607716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9940);