Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C7×C4⋊C8 ⋊ C2 |
| Hall | C3×C7 ⋊ D4⋊C8 |
| Sylow | C7 ⋊ #4483 |
| Sylow | C3 ⋊ #89278 |
164 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 63 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|b^2=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^2,h^a=h^6,d^b=df228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 674);