Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65733 |
| Fitting | C3×C5×D8 ⋊ C4 |
| Hall | C3×C5 ⋊ #444 |
| Sylow | C5 ⋊ C3×#444 |
208 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 80 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)(4,5,6,8,7)(9,12)(10,17)(11,19)(13,23)(14,24)(15,16)(18,21)(20,22);(9,11)(10,16)(12,20)(13,17)(14,22)(15,21)(18,24)(19,23);(5,6,7,8)(9,10,13,18,15,20,14,19)(11,16,17,24,21,12,22,23)87 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10604131, C3×#10604130, #14315811, … |
| maximal normal subgroup of | C3×#10604131, C3×#10604130, #14315811, … |
| maximal quotient of | C3×#10603937, C3×#10604061, C3×#10604792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6461);