Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2254 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^12422 conjugacy classes — view the full character table.
| maximal subgroup of | #15750578, #15750580, #15776883, … |
| maximal normal subgroup of | #15750578, #15750580, #15776883, … |
| maximal quotient of | #15779356, #15780954, #15781520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6792);