Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65326 |
| Fitting | C3×C5×#121 ⋊ C2 |
| Hall | C3×C5 ⋊ #449 |
| Sylow | C5 ⋊ C3×#449 |
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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)(10,12)(14,19)(15,16)(18,20);(9,10)(11,12)(13,15,17,16)(14,18,20,19);(5,6)(7,8)(13,14)(15,18)(16,19)(17,20)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#449, C2×C3×#65326, #14423431, … |
| maximal normal subgroup of | C3×D5×#449, C2×C3×#65326, #14423431, … |
| maximal quotient of | C3×#10600495, C3×#10600490, C3×#10600504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4129);