Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C3×C4×C7 ⋊ C22 |
| Hall | C3×C7 ⋊ #379 |
| Sylow | C7 ⋊ #4955 |
| Sylow | C3 ⋊ #89727 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|c^2=d,c^a=cf,h^a=h^6,c^b=ce,g^b=g^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3608);