Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#65247 |
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #386 |
| Sylow | C5 ⋊ C3×#386 |
572 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)(9,10,11,12)(14,16)(18,20);(17,18)(19,20);(5,6)(7,8)(13,14)(15,16)(18,20)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598709, #14279056, C3×#10600826, … |
| maximal normal subgroup of | C3×#10598709, #14279056, C3×#10600826, … |
| maximal quotient of | C3×#10602337, C3×#10600198, C3×#10600201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4050);