Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #1780 |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^8,c^b=cg,h^b=h^12,h^c=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16777633, #16781463, #16781468, … |
| maximal normal subgroup of | #16777633, #16781463, #16781468, … |
| maximal quotient of | #16781044, #16781047, #16781050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20335);