Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C73×#1555 ⋊ C2 |
| Sylow | C73 ⋊ #8522 |
1102 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 111 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,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fgh,i^b=i^72,f^c=fh,i^c=i^72970 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 62087);