Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65178 |
| Fitting | C3×C5×#107 ⋊ C2 |
| Hall | C3×C5 ⋊ #440 |
| Sylow | C5 ⋊ C3×#440 |
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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)(14,18)(15,20)(17,19);(13,14,15,17,16,19,20,18);(5,6)(7,8)(14,17)(15,20)(18,19)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#440, C2×C3×#65178, #14416392, … |
| maximal normal subgroup of | C3×D5×#440, C2×C3×#65178, #14416392, … |
| maximal quotient of | C3×#10599351, C3×#10599354, C3×#10599355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3981);