Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#575×C73 ⋊ C2 |
| Sylow | C73 ⋊ #61030 |
2796 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|e^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,d^b=df,f^b=fh,i^c=i^72,f^d=fh1642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1044640);