Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2151 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^12,c^b=cg,h^b=h^12296 conjugacy classes — view the full character table.
| maximal subgroup of | #15750323, #15779055, #15779058, … |
| maximal normal subgroup of | #15750323, #15779055, #15779058, … |
| maximal quotient of | #15774468, #15774494, #15774528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6270);