Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#66153 |
| Hall | C3×C5 ⋊ #568 |
| Sylow | C5 ⋊ C3×#568 |
516 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 374 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)(10,15)(14,20)(16,22)(21,24);(11,17)(14,20)(18,23)(21,24);(9,11)(10,14)(12,18)(13,17)(15,20)(16,21)(19,23)(22,24);(5,6)(7,8)(9,10,12,16,13,15,19,22)(11,14,18,21,17,20,23,24)222 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10600794, C3×#10600928, #14299684, … |
| maximal normal subgroup of | C3×#10600794, C3×#10600928, #14299684, … |
| maximal quotient of | C3×#10613933, C3×#10614242, C3×#10615805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10025);