Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D13⋊#443 |
| Fitting | C13×#135 ⋊ C4 |
| Sylow | C13 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^5,e^b=eg,h^c=h^8,h^d=h^12,h^f=h^1298 conjugacy classes — view the full character table.
| maximal subgroup of | #16789508, #16789512, #16789527, … |
| maximal normal subgroup of | #16789508, #16789512, #16789527, … |
| maximal quotient of | D8×D13⋊C8, SD16×D13⋊C8, Q16×D13⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21276);