Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #421×C73 ⋊ C4 |
| Sylow | C73 ⋊ #11085 |
938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=d,f^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^27,c^b=cf,e^b=eh,d^c=dh,f^c=fh,g^c=gh,i^g=i^72448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1092838);