Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65732 |
| Fitting | C3×C5×D8 ⋊ C4 |
| Hall | C3×C5 ⋊ #443 |
| Sylow | C5 ⋊ C3×#443 |
212 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 80 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)(4,5,6,8,7)(9,12)(10,16)(11,17)(13,21)(14,15)(18,19)(20,24)(22,23);(9,11)(10,15)(12,18)(13,19)(14,20)(16,23)(17,22)(21,24);(5,6,7,8)(9,10,13,17,14,18,23,24)(11,15,19,22,20,12,16,21)105 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10604128, C3×#10604122, #14315667, … |
| maximal normal subgroup of | C3×#10604128, C3×#10604122, #14315667, … |
| maximal quotient of | C3×D8×#170, C3×#10603936, C3×#10604060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6460);