Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×Q8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #8429 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=g,d^2=h,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^27,d^b=dh,f^b=fgh,e^c=eg,f^c=fg,i^f=i^72493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1088040);