Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65161 |
| Fitting | C3×C5×#107 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×D8 |
| Sylow | C5 ⋊ C3×C4×D8 |
268 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 102 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)(9,11,12,10)(14,17)(15,20)(18,19);(9,10,12,11)(13,14)(15,17)(16,19)(18,20);(5,6)(7,8)(9,10,12,11)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598609, #14277807, C3×#10598607, … |
| maximal normal subgroup of | C3×#10598609, #14277807, C3×#10598607, … |
| maximal quotient of | C3×#10599349, C3×#10599352, C3×#10599356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3964);