Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #333 |
| Sylow | C7 ⋊ #4546 |
| Sylow | C3 ⋊ #89341 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=d,b^2=ef,c^2=ef,d^2=f,b^a=bc,c^a=ce,g^a=g^2,h^a=h^6,c^b=cef,d^b=df159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 741);