Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #504⋊ΓL(1,𝔽8) |
| Fitting, Hall | C7×#504 ⋊ C3 |
| Sylow | #504 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #504⋊C3 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2,3,2^4,7,2|a^2=c,c^2=d,d^2=h,e^2=h,f^2=h,e^b=ef,f^b=e,g^b=g^2,f^e=fh136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4367);