Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65136 |
| Fitting | C3×C5×C4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #478 |
| Sylow | C5 ⋊ C3×#478 |
204 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(11,15)(17,18,23,24,20,22,19,21);(9,11,12,15)(10,13,14,16)(18,22)(21,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(18,21)(19,23)(22,24)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#478, C2×C3×#65136, #14429944, … |
| maximal normal subgroup of | C3×D5×#478, C2×C3×#65136, #14429944, … |
| maximal quotient of | C3×#10601273, C3×#10599463, C3×#10599464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3939);