Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1143⋊A4 |
| Fitting | C22×C7×Q8 ⋊ C2×C3 |
| Hall | C22×#1143 ⋊ C3 |
| Sylow | C7 ⋊ A4×SD16 |
166 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^2,3,2^4,7|b^2=e,d^2=e,b^a=bd,d^a=de,h^a=h^6,d^b=de,f^c=fg,g^c=f,h^c=h^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6962);