Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C7×#108 ⋊ C2 |
| Hall | C3×C7 ⋊ #471 |
| Sylow | C7 ⋊ #4898 |
| Sylow | C3 ⋊ #89670 |
208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|b^2=e,c^2=e,d^2=f,e^2=f,b^a=be,c^a=cef,e^a=ef,g^a=g^2,h^a=h^6,c^b=cd,d^b=df,d^c=df156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5823);