Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ #490 |
| Sylow | C7 ⋊ #4713 |
| Sylow | C3 ⋊ #89843 |
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 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|a^2=e,c^2=def,d^2=f,e^2=f,b^a=bd,c^a=cf,h^a=h^6,c^b=cdef,d^b=df,e^b=ef,g^b=g^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1568);