Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×C22⋊C4 |
| Sylow | C7 ⋊ #4666 |
| Sylow | C3 ⋊ C4×(C2×D7)⋊C4 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=f,c^2=d,c^a=ce,h^a=h^6,g^b=g^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3542);