Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65430 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #471 |
| Sylow | C5 ⋊ C3×#471 |
208 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11)(10,15)(12,18)(13,19)(14,21)(16,24)(17,20)(22,23);(9,10,12,14,13,16,20,22)(11,15,18,21,19,24,17,23);(5,6)(7,8)(10,14)(11,17)(12,20)(16,22)(18,19)(21,23)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#471, C2×C3×#65430, #14429314, … |
| maximal normal subgroup of | C3×D5×#471, C2×C3×#65430, #14429314, … |
| maximal quotient of | C3×#10601639, C3×#10601731, C3×#10601644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4233);