Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C7 ⋊ #568 |
| Sylow | C7 ⋊ #5819 |
| Sylow | C3 ⋊ #90436 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|b^2=e,e^2=f,d^a=df,h^a=h^6,c^b=cf,g^b=g^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8706);