Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C7 ⋊ #340 |
| Sylow | C7 ⋊ #4529 |
| Sylow | C3 ⋊ #89346 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=e,b^2=c,c^2=f,d^2=f,b^a=bd,c^a=cf,d^a=df,h^a=h^6,g^b=g^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 297);