Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #89242⋊C3 |
| Fitting | C7×C32 ⋊ C2×C3 |
| Hall | #89242 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ M64 |
| Sylow | C7 ⋊ C3×M64 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^2,3,2^4,7|b^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,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, 8);