Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C73×#1515 ⋊ C2 |
| Sylow | C73 ⋊ #17598 |
996 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,e^2=h,b^a=be,c^a=ch,e^a=eg,i^a=i^72,e^b=eh,f^b=fgh,i^b=i^72,d^c=dg,i^c=i^72,i^d=i^72985 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 137115);