Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65490 |
| Fitting | C3×C5×AGL(1,ℤ/8) ⋊ C2 |
| Hall | C3×C5 ⋊ #454 |
| Sylow | C5 ⋊ C3×#454 |
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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)(10,16)(11,19)(12,13)(17,18)(20,21)(22,23);(9,11,14,21)(10,15,18,24)(12,20,13,19)(16,23,17,22);(5,6)(7,8)(9,10)(11,15)(12,16)(13,17)(14,18)(19,22)(20,23)(21,24)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#454, C2×C3×#65490, #14425087, … |
| maximal normal subgroup of | C3×D5×#454, C2×C3×#65490, #14425087, … |
| maximal quotient of | C3×#10601763, C3×#10601771, C3×#10601764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4293);