Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#4647 |
| Hall | C3×C5 ⋊ #389 |
| Sylow | C3 ⋊ C5×#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)(6,7,8)(9,10,11,12)(14,16)(17,19,20,18);(13,14,15,16)(18,19);(7,8)(17,18,20,19)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#389, C2×C5×#4647, D5×#4647, … |
| maximal normal subgroup of | C5×D3×#389, C2×C5×#4647, D5×#4647, … |
| maximal quotient of | C5×Dic3⋊#95, C5×#69406, C5×#69407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4341);