Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3079 |
416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^12,f^c=fg272 conjugacy classes — view the full character table.
| maximal subgroup of | #15758768, #15758770, #15758775, … |
| maximal normal subgroup of | #15758768, #15758770, #15758775, … |
| maximal quotient of | #15862414, #15863896, #15865104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14325);