Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C73 ⋊ C8 |
| Sylow | C73 ⋊ #7333 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,b^a=be,d^a=dgh,f^a=fh,c^b=cgh,e^b=eh,i^b=i^63,d^c=dh,i^d=i^27,i^f=i^72334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116592);