Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | D13⋊#568 |
| Sylow | C13 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,d^a=dg,h^a=h^8,c^b=cg,h^e=h^12,h^f=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16785351, #16785356, #16785365, … |
| maximal normal subgroup of | #16785351, #16785356, #16785365, … |
| maximal quotient of | #16808010, #16808019, C4×#11719621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21502);