Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#65021 |
| Fitting | C3×C5×C22⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #447 |
| Sylow | C5 ⋊ C3×#447 |
396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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)(4,5,7,8,6)(10,12)(13,14,18,20,16,19,15,17);(9,10)(11,12);(5,6)(7,8)(14,17)(15,18)(19,20)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599077, C3×#10598899, #14287707, … |
| maximal normal subgroup of | C3×#10599077, C3×#10598899, #14287707, … |
| maximal quotient of | C3×#10598899, C3×#10598924, C3×#10598903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3824);