Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#65903 |
| Hall | C3×C5 ⋊ #557 |
| Sylow | C5 ⋊ C3×#557 |
400 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 226 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,13,14,15)(17,20,21,19)(18,22,23,24);(17,19,21,20)(18,22,23,24);(17,18,21,23)(19,24,20,22);(5,6)(7,8)(9,10,12,14)(11,15,16,13)195 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612311, C3×#10611431, #14472118, … |
| maximal normal subgroup of | C3×#10612311, C3×#10611431, #14472118, … |
| maximal quotient of | C3×Q8×#683, C3×#10614192, C3×#10614191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9775);