Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊#1057 |
| Sylow | C13 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^8,d^b=df,h^c=h^8,h^e=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16⋊#1057, D13⋊(SD16⋊C8), #16795203, … |
| maximal normal subgroup of | C2×SD16⋊#1057, D13⋊(SD16⋊C8), #16795203, … |
| maximal quotient of | #16780582, #16780586, #16780958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20099);