Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4856 |
| Hall | C3×C5 ⋊ #501 |
| Sylow | C3 ⋊ C5×#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)(6,7,8)(9,11,12,16)(10,13,14,15)(18,22)(19,23)(21,24);(17,18,19,22,20,21,23,24);(7,8)(9,10,12,14)(11,15,16,13)(18,21)(22,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#501, C2×C5×#4856, D5×#4856, … |
| maximal normal subgroup of | C5×D3×#501, C2×C5×#4856, D5×#4856, … |
| maximal quotient of | C5×#70556, C5×#70561, C5×#68860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4550);