Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C42×C7 ⋊ C22 |
| Hall | C3×C7 ⋊ #421 |
| Sylow | C7 ⋊ #5005 |
| Sylow | C3 ⋊ #89593 |
308 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|c^2=d,e^2=f,c^a=cf,h^a=h^6,c^b=ce,d^b=df,e^b=ef,g^b=g^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1777);