Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D13⋊M64 |
| Sylow | C13 ⋊ C2×M64 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^8,h^c=h^12,h^d=h^12176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777991, #16777994, #16777997, … |
| maximal normal subgroup of | #16777991, #16777994, #16777997, … |
| maximal quotient of | #16791138, #16791143, #16791144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20931);