Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| unambiguous semidirect product | #11924040⋊C16 |
| Sylow | C73 ⋊ #7052 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,f^2=h,b^a=bg,i^a=i^10,i^c=i^27,i^e=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116335);