Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #90191⋊C3 |
| Hall | #90191 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #544 |
| Sylow | C7 ⋊ C3×#544 |
412 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^4,3,2^2,7|a^2=g,b^2=g,c^2=g,b^a=bg,c^a=cg,d^a=df,h^a=h^6,c^b=cf,h^e=h^286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6524);