Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #362 |
| Sylow | C7 ⋊ #4517 |
| Sylow | C3 ⋊ #89312 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=c,c^2=ef,d^2=ef,e^2=f,b^a=bd,c^a=ce,d^a=de,e^a=ef,g^a=g^2,h^a=h^6,d^b=df216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 710);