Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65038 |
| Fitting | C3×C5×#100 ⋊ C2 |
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ C3×#472 |
216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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)(11,18)(12,20)(14,21)(16,17)(22,23);(9,11,12,19,13,18,20,24)(10,14,16,22,17,23,15,21);(5,6)(7,8)(9,10)(11,14)(12,16)(13,17)(15,20)(18,23)(19,22)(21,24)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#472, C2×C3×#65038, #14429422, … |
| maximal normal subgroup of | C3×D5×#472, C2×C3×#65038, #14429422, … |
| maximal quotient of | C3×#10599188, C3×#10599202, C3×#10599290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3841);