Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5049 |
| Fitting | C3×C5×C22⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #468 |
| Sylow | C3 ⋊ C5×#468 |
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 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)(13,14,16,18)(15,20,19,17);(9,10)(11,12)(14,18)(17,20);(7,8)(10,12)(14,17)(15,19)(18,20)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#468, C2×C5×#5049, D5×#5049, … |
| maximal normal subgroup of | C5×D3×#468, C2×C5×#5049, D5×#5049, … |
| maximal quotient of | C5×#71104, C5×#71120, C5×#71136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4743);