Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#6471 |
| Fitting | C3×C7×M16 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×AGL(1,ℤ/8) |
| Sylow | C7 ⋊ D3×AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C2×#6471 |
596 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
123 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#89519, D3×D7×AGL(1,ℤ/8), D3×#89594, … |
| maximal normal subgroup of | D3×#89519, D3×D7×AGL(1,ℤ/8), D3×#89594, … |
| maximal quotient of | #72245859 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8543);