Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#88034 |
| Sylow | C13 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^12464 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#88034, #15750358, #15750360, … |
| maximal normal subgroup of | D4⋊#88034, #15750358, #15750360, … |
| maximal quotient of | #15750585, #15750592, #15750606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2706);