Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C7 ⋊ #552 |
| Sylow | C7 ⋊ #5541 |
| Sylow | C3 ⋊ #90272 |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|b^2=f,c^2=e,d^2=f,c^a=cf,d^a=df,h^a=h^6,d^b=def,g^b=g^2153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 7058);