Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1985 |
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^5,c^b=cg,h^b=h^8,h^c=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16777667, #16781456, #16781458, … |
| maximal normal subgroup of | #16777667, #16781456, #16781458, … |
| maximal quotient of | #16785040, #16785043, #16785046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20684);