Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1738 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^8,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16785356, #16785358, #16785359, … |
| maximal normal subgroup of | #16785356, #16785358, #16785359, … |
| maximal quotient of | #16778998, #16779001, #16779008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20203);