Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q16×C73 ⋊ C8 |
| Sylow | C73 ⋊ #17856 |
678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=fg,e^2=g,f^2=h,b^a=be,d^a=dg,e^a=eg,i^a=i^63,e^b=eg,d^c=dg,i^c=i^10,i^f=i^27,i^h=i^72214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118117);