Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65422 |
| Fitting | C2×C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #417 |
| Sylow | C5 ⋊ C3×#417 |
324 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(9,10,11,12)(13,16,15,14,18,20,17,19);(13,15,18,17)(14,16,19,20);(5,6)(7,8)(13,14)(15,16)(17,20)(18,19)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601177, C3×#10600879, #14297208, … |
| maximal normal subgroup of | C3×#10601177, C3×#10600879, #14297208, … |
| maximal quotient of | C3×#10601548, C3×#10600645, C3×#10600647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4225);