Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊C4)⋊C16 |
| unambiguous semidirect product | (Dic7⋊C16)⋊C3 |
| Hall | Dic7⋊C16 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4⋊C16 |
| Sylow | C7 ⋊ C3×C4⋊C16 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^2,3,2^4,7|a^2=e,b^2=d,d^2=f,f^2=g,b^a=be,h^a=h^6,h^c=h^2152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 62);