Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#65501 |
| Hall | C3×C5 ⋊ #380 |
| Sylow | C5 ⋊ C3×#380 |
468 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)(14,16);(17,18,19,20);(5,6)(7,8)(9,10,11,12)(13,14)(15,16)(18,20)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598116, C3×#10598167, #14277046, … |
| maximal normal subgroup of | C3×#10598116, C3×#10598167, #14277046, … |
| maximal quotient of | C3×#10602920, C3×#10602327, C3×#10602328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4304);