Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×SD32 ⋊ C4 |
| Sylow | C13 ⋊ #2175 |
160 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^5,d^b=df,f^b=fg,h^c=h^8,h^e=h^1265 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13131232, #16807194, #261×#509, … |
| maximal normal subgroup of | C2×#13131232, #16807194, #261×#509, … |
| maximal quotient of | #16788801, #16788802, #16788803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20906);