Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#6502⋊C3 |
| unambiguous semidirect product | (C2×#6502)⋊C3 |
| Fitting | C22×C7×D4 ⋊ C2×C3 |
| Hall | C2×#6502 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#121 |
| Sylow | C7 ⋊ C2×C3×#121 |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #72259870, C2×#121×AGL(1,𝔽7) |
| maximal normal subgroup of | #72259870, C2×#121×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6816);