Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#65526 |
| Hall | C3×C5 ⋊ #413 |
| Sylow | C5 ⋊ C3×#413 |
300 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 134 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)(10,15)(11,17)(12,19)(20,24);(9,11)(10,14)(12,18)(13,17)(15,21)(16,20)(19,23)(22,24);(5,6)(7,8)(9,10,12,16,13,15,19,22)(11,14,18,20,17,21,23,24)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598191, C3×#10598184, #14279105, … |
| maximal normal subgroup of | C3×#10598191, C3×#10598184, #14279105, … |
| maximal quotient of | C3×#10602364, C3×#10602393, C3×#10602365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4329);