Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#66047 |
| Hall | C3×C5 ⋊ #559 |
| Sylow | C5 ⋊ C3×#559 |
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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 — 4 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(13,16)(17,19,20,24)(18,21,22,23);(11,15)(13,16)(19,24)(21,23);(9,11)(10,13)(12,15)(14,16)(19,24)(21,23);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,20,22)(19,23,24,21)159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602077, C3×#10599195, #14288860, … |
| maximal normal subgroup of | C3×#10602077, C3×#10599195, #14288860, … |
| maximal quotient of | C3×#10606056, C3×#10608034, C3×#10614904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9919);