Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×C4⋊C4 |
| Sylow | C7 ⋊ C4×Dic3⋊C4 |
| Sylow | C3 ⋊ #89421 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=e,c^2=d,h^a=h^6,c^b=cef,g^b=g^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3172);