Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D13⋊#504 |
| Sylow | C13 ⋊ C2×#504 |
368 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=e,e^2=f,f^2=g,h^a=h^8,c^b=cg,h^d=h^12,h^e=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16789373, #16789379, #16790563, … |
| maximal normal subgroup of | #16789373, #16789379, #16790563, … |
| maximal quotient of | #16806724, #16806736, #16806737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21475);