Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#6090 |
| Sylow | C13 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^12,c^b=ce296 conjugacy classes — view the full character table.
| maximal subgroup of | D13×Q8⋊C16, C2×Q8⋊#6090, #15772720, … |
| maximal normal subgroup of | D13×Q8⋊C16, C2×Q8⋊#6090, #15772720, … |
| maximal quotient of | #15749701, #15749731, #15749823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2489);