Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65417 |
| Fitting | C2×C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #436 |
| Sylow | C5 ⋊ C3×#436 |
244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(13,14,15,18,16,17,19,20);(10,12)(14,17)(18,20);(5,6)(7,8)(9,10)(11,12)(14,17)(18,20)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#436, C2×C3×#65417, #14414843, … |
| maximal normal subgroup of | C3×D5×#436, C2×C3×#65417, #14414843, … |
| maximal quotient of | C3×#10601652, C3×#10601659, C3×#10601743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4220);