Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#66171 |
| Fitting | C3×C5×2−1+4 ⋊ 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)(9,11,13,18)(10,15,14,21)(12,20,19,17)(16,24,22,23);(10,14)(15,21)(16,22)(23,24);(9,10)(11,15)(12,16)(13,14)(17,23)(18,21)(19,22)(20,24);(5,6)(7,8)(11,17)(12,19)(15,23)(16,22)(18,20)(21,24)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10615746, C3×#10612018, #14457699, … |
| maximal normal subgroup of | C3×#10615746, C3×#10612018, #14457699, … |
| maximal quotient of | C3×#10614294, C3×#10615842, C3×#10614292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10043);