Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C73×#1305 ⋊ C2 |
| Sylow | C73 ⋊ #8756 |
546 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 546 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) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=d,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,i^b=i^72,e^c=eg,f^c=fh970 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 63100);