Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C7×C8 ⋊ C22 |
| Hall | C3×C7 ⋊ #575 |
| Sylow | C7 ⋊ #5768 |
| Sylow | C3 ⋊ #90459 |
524 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 128 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=f,d^2=e,e^2=f,d^a=de,e^a=ef,h^a=h^6,d^b=def,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, 8496);