Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C4⋊Q8) |
| unambiguous semidirect product | (D7×C4⋊Q8)⋊C3 |
| Fitting | C7×C4⋊Q8 ⋊ C2×C3 |
| Hall | D7×C4⋊Q8 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C4⋊Q8 |
| Sylow | C7 ⋊ C2×C3×C4⋊Q8 |
580 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 236 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#492, AGL(1,𝔽7)×#532, AGL(1,𝔽7)×#498, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#492, AGL(1,𝔽7)×#532, AGL(1,𝔽7)×#498, … |
| maximal quotient of | AGL(1,𝔽7)×#498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6747);