Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C7 ⋊ #365 |
| Sylow | C7 ⋊ #4494 |
| Sylow | C3 ⋊ #89282 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|a^2=d,b^2=de,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,h^a=h^6,c^b=ce,d^b=df,e^b=ef,g^b=g^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 253);