Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65492 |
| Fitting | C3×C5×#137 ⋊ C2 |
| Hall | C3×C5 ⋊ #471 |
| Sylow | C5 ⋊ C3×#471 |
208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 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)(9,11,14,21)(10,16,17,24)(12,20,13,18)(15,23,22,19);(9,10)(11,19)(12,15)(13,22)(14,17)(16,20)(18,24)(21,23);(5,6)(7,8)(10,15)(11,18)(12,13)(17,22)(19,23)(20,21)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#471, C2×C3×#65492, #14429317, … |
| maximal normal subgroup of | C3×D5×#471, C2×C3×#65492, #14429317, … |
| maximal quotient of | C3×#10601893, C3×#10601909, C3×#10601829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4295);