Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1850 |
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^12,h^b=h^12296 conjugacy classes — view the full character table.
| maximal subgroup of | #15756886, #15756887, #15756891, … |
| maximal normal subgroup of | #15756886, #15756887, #15756891, … |
| maximal quotient of | #15756749, #15756754, #15756760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4690);