Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#65520 |
| Fitting | C22×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #393 |
| Sylow | C5 ⋊ C3×#393 |
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,12)(17,19,20,24)(18,21,22,23);(14,16)(17,18,20,22)(19,23,24,21);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598829, #14278267, C3×#10601765, … |
| maximal normal subgroup of | C3×#10598829, #14278267, C3×#10601765, … |
| maximal quotient of | C3×#10602363, C3×#10602360, C3×#10602927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4323);