Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65756 |
| Hall | C3×C5 ⋊ #407 |
| Sylow | C5 ⋊ C3×#407 |
380 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 116 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)(4,5,6,8,7)(13,15,17,16)(14,18,19,20);(10,12);(5,6,7,8)(9,10)(11,12)(13,14,16,18,17,19,15,20)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598503, #14276922, C3×#10598767, … |
| maximal normal subgroup of | C3×#10598503, #14276922, C3×#10598767, … |
| maximal quotient of | C3×#10604202, C3×#10604292, C3×#10604203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6484);