Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ #489 |
| Sylow | C7 ⋊ #5055 |
| Sylow | C3 ⋊ #89486 |
200 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|b^2=d,c^2=def,d^2=f,e^2=f,b^a=be,c^a=cde,d^a=df,e^a=ef,h^a=h^6,c^b=cf,g^b=g^2138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1551);