Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | #15783534, #15783537, #15783597, … |
| maximal normal subgroup of | #15783534, #15783537, #15783597, … |
| maximal quotient of | #15783358, #15783365, #15783427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6827);