Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1916 |
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^8,h^b=h^8,h^f=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13130889, D13⋊#1916, #16798722, … |
| maximal normal subgroup of | C2×#13130889, D13⋊#1916, #16798722, … |
| maximal quotient of | #16784231, #16784235, #16784239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20563);