Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D73⋊#1347 |
| Fitting | #466×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#1347 |
558 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,d^2=gh,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^27,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^c=i^72,i^e=i^72454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1094322);