Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #90325⋊C3 |
| Fitting | C7×C22⋊Q8 ⋊ C2×C3 |
| Hall | #90325 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #543 |
| Sylow | C7 ⋊ C3×#543 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^4,3,2^2,7|c^2=f,d^2=f,d^a=dg,h^a=h^6,c^b=cg,d^c=df,h^e=h^280 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#543, #72277502, #72277516, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#543, #72277502, #72277516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6659);