Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D7×#932 |
| Fitting | C2×C3×C7×D4 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×AGL(1,ℤ/8) |
| Sylow | C7 ⋊ C2×#932 |
| Sylow | C3 ⋊ D7×AGL(1,ℤ/8) |
596 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#5077, D3×D7×AGL(1,ℤ/8), D7×#5198, … |
| maximal normal subgroup of | D7×#5077, D3×D7×AGL(1,ℤ/8), D7×#5198, … |
| maximal quotient of | C3×D7×#932, #72269404 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 9386);