Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #344×C73 ⋊ C4 |
| Sylow | C73 ⋊ #11301 |
554 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=de,c^2=d,e^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^27,c^b=cf,d^b=dh,e^b=eh,g^b=gh,f^c=fh,g^c=gh,i^g=i^72442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1093102);