Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×#99×C73 ⋊ C4 |
| Sylow | C73 ⋊ #10960 |
1526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^46,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh,i^c=i^27,i^f=i^72460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1092653);