Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#261)⋊C16 |
| Fitting | C2×C13×C16 ⋊ C4 |
| Sylow | C13 ⋊ #1374 |
160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^b=h^8,h^e=h^12176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#261)⋊C16, #16789043, #16789047, … |
| maximal normal subgroup of | C2×(C2×#261)⋊C16, #16789043, #16789047, … |
| maximal quotient of | #16777082, #16777096, #16777106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19547);