Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C8×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C22⋊C8) |
| unambiguous semidirect product | (D7×C22⋊C8)⋊C3 |
| Fitting | C7×C22⋊C8 ⋊ C2×C3 |
| Hall | D7×C22⋊C8 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C22⋊C8 |
| Sylow | C7 ⋊ C2×C3×C22⋊C8 |
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#447, AGL(1,𝔽7)×#450, AGL(1,𝔽7)×#407 |
| maximal normal subgroup of | AGL(1,𝔽7)×#447, AGL(1,𝔽7)×#450, AGL(1,𝔽7)×#407 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 914);