Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #1869 |
432 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 104 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=df,f^2=g,b^a=bd,c^a=ce,h^a=h^8,h^b=h^8,h^c=h^12,h^f=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16777410, #16777443, #16781177, … |
| maximal normal subgroup of | #16777410, #16777443, #16781177, … |
| maximal quotient of | #16782712, #16782716, #16782720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20484);