Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#65764 |
| Fitting | C22×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #381 |
| Sylow | C5 ⋊ C3×#381 |
436 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,6,8,7)(10,12)(13,15,16,19)(14,18,17,20);(14,17)(18,20);(5,6,7,8)(9,10)(11,12)(13,14)(15,18)(16,17)(19,20)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598692, C3×#10598553, #14276923, … |
| maximal normal subgroup of | C3×#10598692, C3×#10598553, #14276923, … |
| maximal quotient of | C3×#10604909, C3×#10604197, C3×#10604255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6492);