Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C42×C7 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×#126 |
| Sylow | C7 ⋊ D3×#126 |
| Sylow | C3 ⋊ D7×#126 |
492 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 130 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=e,d^2=f,c^a=cf,d^a=def,h^a=h^6,c^b=cf,d^b=def,g^b=g^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 7287);