Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#64936 |
| Hall | C3×C5 ⋊ #389 |
| Sylow | C5 ⋊ C3×#389 |
340 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)(14,16)(17,19,20,18);(13,14,15,16)(18,19);(5,6)(7,8)(17,18,20,19)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#389, C2×C3×#64936, #14320756, … |
| maximal normal subgroup of | C3×D5×#389, C2×C3×#64936, #14320756, … |
| maximal quotient of | C3×#10600197, C3×#10600199, C3×#10600200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3739);