Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#64938 |
| Hall | C3×C5 ⋊ C4×C4⋊C4 |
| Sylow | C5 ⋊ C3×C4×C4⋊C4 |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(13,15,16,14)(18,20);(13,14,16,15)(17,18,19,20);(5,6)(7,8)(13,14,16,15)240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598509, #14277339, C3×#10599070, … |
| maximal normal subgroup of | C3×#10598509, #14277339, C3×#10599070, … |
| maximal quotient of | C3×Dic5×#95, C3×#10600195, C3×#10600197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3741);