Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C73 ⋊ C8 |
| Sylow | C73 ⋊ #17787 |
778 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=e,d^2=g,e^2=g,f^2=h,b^a=be,e^a=eg,i^a=i^10,c^b=cg,i^f=i^27,i^h=i^72268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118100);