Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×H(5,𝔽2) ⋊ C2×C3 |
| Hall | #90526 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #576 |
| Sylow | C7 ⋊ C3×#576 |
536 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^4,3,2^2,7|f^2=g,d^a=df,f^a=fg,h^a=h^6,c^b=cg,f^d=fg,h^e=h^283 conjugacy classes — view the full character table.
| maximal subgroup of | #72229639, AGL(1,𝔽7)×#576, #72229670, … |
| maximal normal subgroup of | #72229639, AGL(1,𝔽7)×#576, #72229670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6858);