Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×#4866 |
| Fitting | C3×C5×#106 ⋊ C2 |
| Hall | C3×C5 ⋊ #482 |
| Sylow | C3 ⋊ C5×#482 |
212 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,14)(13,16)(17,19,21,18,20,23,24,22);(9,11,12,15)(10,13,14,16)(17,18,20,22)(19,24,23,21);(7,8)(9,10)(11,13)(12,14)(15,16)(18,22)(19,23)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#482, C2×C5×#4866, D5×#4866, … |
| maximal normal subgroup of | C5×D3×#482, C2×C5×#4866, D5×#4866, … |
| maximal quotient of | C5×#68873, C5×#70580, C5×#68881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4560);