Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C4 |
| direct product | C3×#64992 |
| Hall | C3×C5 ⋊ #491 |
| Sylow | C5 ⋊ C3×#491 |
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,7,8,6)(10,14)(13,15)(17,19,27,31,21,26,20,28)(18,23,29,32,22,30,24,25);(9,11,12,16)(10,13,14,15)(18,22)(19,26)(24,29)(28,31);(5,6)(7,8)(9,10,12,14)(11,15,16,13)(17,18,21,22)(19,25,26,32)(20,29,27,24)(23,31,30,28)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598012, #14278378, C3×#10598542, … |
| maximal normal subgroup of | C3×#10598012, #14278378, C3×#10598542, … |
| maximal quotient of | C3×#10600608, C3×#10600610, C3×#10600615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3795);