Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65139 |
| Hall | C3×C5 ⋊ #477 |
| Sylow | C5 ⋊ C3×#477 |
192 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 192 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) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(11,15)(17,20,21,18,22,23,19,24);(9,11,12,15)(10,13,14,16)(17,19,22,21)(18,23,24,20);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,22,24)(19,23,21,20)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599197, C3×#10599053, #14289409, … |
| maximal normal subgroup of | C3×#10599197, C3×#10599053, #14289409, … |
| maximal quotient of | C3×#10601278, C3×#10599476, C3×#10599417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3942);