Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×C7×C22⋊C4 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×#124 |
| Sylow | C7 ⋊ D3×#124 |
| Sylow | C3 ⋊ D7×#124 |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=f,d^2=f,c^a=cf,d^a=df,h^a=h^6,c^b=cf,d^b=df,g^b=g^2,d^c=de114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 7343);