Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×D7×D8 |
| Fitting | C3×C7×D8 ⋊ C22 |
| Hall | C3×C7 ⋊ C22×D8 |
| Sylow | C7 ⋊ C2×D3×D8 |
| Sylow | C3 ⋊ C2×D7×D8 |
676 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×AGL(1,ℤ/8), D3×D8×AGL(1,𝔽7), D7×#63926, … |
| maximal normal subgroup of | D3×D7×AGL(1,ℤ/8), D3×D8×AGL(1,𝔽7) |
| maximal quotient of | D7×#63926, D3×#13096364 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8561);