Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×Q16 |
| Sylow | C7 ⋊ #4873 |
| Sylow | C3 ⋊ #89645 |
220 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=f,b^2=ef,c^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=h^6,c^b=cef,e^c=ef168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5817);