Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65337 |
| Fitting | C3×C5×C22⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #465 |
| Sylow | C5 ⋊ C3×#465 |
248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 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)(13,14,16,18)(15,20,19,17);(9,10)(11,12);(5,6)(7,8)(10,12)(14,17)(15,19)(18,20)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#465, C2×C3×#65337, #14427622, … |
| maximal normal subgroup of | C3×D5×#465, C2×C3×#65337, #14427622, … |
| maximal quotient of | C3×#10601893, C3×#10601909, C3×#10601925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4140);