Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65163 |
| Hall | C3×C5 ⋊ #500 |
| Sylow | C5 ⋊ C3×#500 |
196 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,13,14,15)(18,21)(19,24)(22,23);(17,18,19,22,20,23,24,21);(5,6)(7,8)(9,10,12,14)(11,15,16,13)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598617, #14278518, C3×#10598618, … |
| maximal normal subgroup of | C3×#10598617, #14278518, C3×#10598618, … |
| maximal quotient of | C3×#10601399, C3×#10601404, C3×#10599652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3966);