Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4851 |
| Hall | C3×C5 ⋊ #475 |
| Sylow | C3 ⋊ C5×#475 |
192 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 90 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)(10,14)(11,15)(17,19,20,18,21,22,24,23);(9,11,12,15)(10,13,14,16);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,21,23)(19,24,22,20)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68406, C5×#68262, #14289995, … |
| maximal normal subgroup of | C5×#68406, C5×#68262, #14289995, … |
| maximal quotient of | C5×#70485, C5×#68684, C5×#68622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4545);