Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D21⋊#95 |
| Hall | C3×C7 ⋊ C2×#95 |
| Sylow | C7 ⋊ D3×#95 |
| Sylow | C3 ⋊ D7×#95 |
660 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=f,c^2=d,c^a=ce,h^a=h^6,c^b=ce,g^b=g^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3548);