Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C73 ⋊ C8 |
| Sylow | C73 ⋊ #9095 |
546 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=df,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^63,d^b=dg,e^b=eg,f^b=fg,i^b=i^10,d^c=dg,e^c=eg,f^c=fg,i^f=i^27,i^h=i^72163 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116974);