Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊#11924040 |
| Sylow | C73 ⋊ SD16⋊C16 |
232 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=cf,d^a=df,i^a=i^10,d^b=df,i^c=i^10,i^e=i^27,i^g=i^72214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1117566);