Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ #494 |
| Sylow | C7 ⋊ #4699 |
| Sylow | C3 ⋊ #89471 |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=e,c^2=df,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^6342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5625);