Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #343 |
| Sylow | C7 ⋊ #4554 |
| Sylow | C3 ⋊ #89349 |
196 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 92 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,b^2=c,c^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,h^a=h^6,d^b=df,e^b=ef,g^b=g^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 304);