Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C73×#2129 ⋊ C2 |
| Sylow | C73 ⋊ #33555 |
1146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^72,d^b=dh,f^b=fgh,i^b=i^72,e^c=eg,i^c=i^72,f^e=fh862 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 323670);