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 ⋊ #366 |
| Sylow | C7 ⋊ #4489 |
| Sylow | C3 ⋊ #89284 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=d,b^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,h^a=h^6,c^b=ce,e^b=ef,g^b=g^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 257);