Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C7×Q8 ⋊ C2×C3 |
| Hall | #90003 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #393 |
| Sylow | C7 ⋊ C3×#393 |
404 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 104 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:
2^3,3,2^3,7|b^2=f,c^2=f,b^a=bg,c^a=ce,h^a=h^6,c^b=cf,h^d=h^286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1420);