Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊Dic7)⋊A4 |
| Hall | C22×C22⋊Dic7 ⋊ C3 |
| Sylow | C7 ⋊ A4×C22⋊C4 |
338 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 49 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|a^2=e,b^a=bd,h^a=h^6,f^c=fg,g^c=f,h^c=h^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6975);