Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66170 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C2 |
| Hall | C3×C5 ⋊ #577 |
| Sylow | C5 ⋊ C3×#577 |
516 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 214 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,13,15,12)(10,18,19,24)(11,20,14,21)(16,17,23,22);(9,12,15,13)(10,17,19,22)(11,20,14,21)(16,18,23,24);(9,11,15,14)(10,16,19,23)(12,21,13,20)(17,24,22,18);(5,6)(7,8)(9,10)(11,16)(12,17)(13,22)(14,23)(15,19)(18,20)(21,24)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10612011, C3×#10615740, #14457715, … |
| maximal normal subgroup of | C3×#10612011, C3×#10615740, #14457715, … |
| maximal quotient of | C3×#10615830, C3×#10614301, C3×#10614292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10042);