Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #89244⋊C3 |
| Fitting | C7×C32 ⋊ C2×C3 |
| Hall | #89244 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ SD64 |
| Sylow | C7 ⋊ C3×SD64 |
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=deg,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,h^a=h^6,h^c=h^289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 9);