Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D13⋊#421 |
| Fitting | C2×C13×#41 ⋊ C4 |
| Sylow | C13 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^8,e^b=eg,h^d=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16785448, #16785450, #16785454, … |
| maximal normal subgroup of | #16785448, #16785450, #16785454, … |
| maximal quotient of | D13⋊#1478, D13⋊#1479, D13⋊#1477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21137);