Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1313 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^8,c^b=cg,h^c=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129754, #16786608, #16786614, … |
| maximal normal subgroup of | C2×#13129754, #16786608, #16786614, … |
| maximal quotient of | #16776917, #16777085, #16777698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19428);