Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#4987 |
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #380 |
| Sylow | C3 ⋊ C5×#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)(6,7,8)(9,10,11,12)(14,16)(18,20);(17,18,19,20);(7,8)(13,14)(15,16)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#70198, #14296992, C5×#70266, … |
| maximal normal subgroup of | C5×#70198, #14296992, C5×#70266, … |
| maximal quotient of | C5×(C2×D3)⋊#95, C5×#69402, C5×#71563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4681);