Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D13⋊#408 |
| Sylow | C13 ⋊ C2×#408 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,h^a=h^8,c^b=cg,h^d=h^12,h^f=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16785368, #16785370, #16785385, … |
| maximal normal subgroup of | #16785368, #16785370, #16785385, … |
| maximal quotient of | D13⋊#1468, D13⋊#1469, D13⋊#1470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21091);