Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1359 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=f,d^2=efg,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^8,c^b=cf,d^b=defg,e^b=eg,h^b=h^12,h^d=h^1265 conjugacy classes — view the full character table.
| maximal subgroup of | #16778159, #16778160, #16778161, … |
| maximal normal subgroup of | #16778159, #16778160, #16778161, … |
| maximal quotient of | #16776999, #16777000, #16777023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19521);