Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65431 |
| Fitting | C3×C5×#131 ⋊ C2 |
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ C3×#472 |
216 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 216 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)(10,16)(12,19)(13,20)(14,21)(15,18)(17,24)(22,23);(9,10,15,22,13,17,12,14)(11,16,18,23,20,24,19,21);(5,6)(7,8)(10,14)(11,18)(12,15)(17,22)(19,20)(21,23)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602915, C3×#10599919, #14316411, … |
| maximal normal subgroup of | C3×#10602915, C3×#10599919, #14316411, … |
| maximal quotient of | C3×#10601640, C3×#10601732, C3×#10601646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4234);