Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C4×#131×C73 ⋊ C2 |
| Sylow | C73 ⋊ #60622 |
2178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|b^2=g,c^2=f,f^2=h,g^2=h,b^a=bf,c^a=cg,f^a=fh,g^a=gh,i^a=i^72,e^d=eh2944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1038912);