Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #90453⋊C3 |
| Fitting | C2×C7×SD16 ⋊ C2×C3 |
| Hall | #90453 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #577 |
| Sylow | C7 ⋊ C3×#577 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^4,3,2^2,7|d^2=g,f^2=g,b^a=bg,h^a=h^6,d^c=df,f^c=fg,f^d=fg,h^e=h^280 conjugacy classes — view the full character table.
| maximal subgroup of | #72229363, AGL(1,𝔽7)×#577, #72229639, … |
| maximal normal subgroup of | #72229363, AGL(1,𝔽7)×#577, #72229639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6785);