Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65184 |
| Fitting | C3×C5×#108 ⋊ C2 |
| Hall | C3×C5 ⋊ #443 |
| Sylow | C5 ⋊ C3×#443 |
212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 212 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) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12,13,22,14,20,23,15)(10,16,17,24,19,11,18,21);(9,11,13,21,14,16,23,24)(10,15,18,20,19,22,17,12);(5,6)(7,8)(9,10)(11,20)(12,16)(13,17)(14,19)(15,21)(18,23)(22,24)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598623, #14277899, C3×#10598624, … |
| maximal normal subgroup of | C3×#10598623, #14277899, C3×#10598624, … |
| maximal quotient of | C3×#10599349, C3×#10599309, C3×#10599350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3987);