Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65369 |
| Hall | C3×C5 ⋊ #501 |
| Sylow | C5 ⋊ C3×#501 |
180 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 180 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) = 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)(18,22)(19,24)(21,23);(9,10,12,14)(11,15,16,13)(18,21)(22,23);(5,6)(7,8)(17,18,19,23,20,21,24,22)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602123, C3×#10602184, #14291049, … |
| maximal normal subgroup of | C3×#10602123, C3×#10602184, #14291049, … |
| maximal quotient of | C3×#10600371, C3×#10600413, C3×#10600414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4172);