Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #556×C73 ⋊ C4 |
| Sylow | C73 ⋊ #8434 |
760 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=h,c^2=h,d^2=h,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^27,d^b=dh,f^b=fgh,i^b=i^72,e^c=eg,f^c=fg,i^f=i^72493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1088051);