Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5057 |
| Fitting | C3×C5×#124 ⋊ C2 |
| Hall | C3×C5 ⋊ #463 |
| Sylow | C3 ⋊ C5×#463 |
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,14)(15,20)(16,18)(17,19);(9,10,11,12)(14,18)(17,20);(7,8)(14,17)(15,19)(18,20)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#463, C2×C5×#5057, D5×#5057, … |
| maximal normal subgroup of | C5×D3×#463, C2×C5×#5057, D5×#5057, … |
| maximal quotient of | C5×#71200, C5×#71232, C5×#71201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4751);