Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65010 |
| Hall | C3×C5 ⋊ #483 |
| Sylow | C5 ⋊ C3×#483 |
208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 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)(11,15)(13,16)(17,18,19,21,20,22,23,24);(9,11)(10,13)(12,15)(14,16);(5,6)(7,8)(9,10,12,14)(11,13,15,16)(18,21)(19,23)(22,24)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599113, C3×#10598909, #14288310, … |
| maximal normal subgroup of | C3×#10599113, C3×#10598909, #14288310, … |
| maximal quotient of | C3×#10600717, C3×#10600721, C3×#10600723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3813);