Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #336×C73 ⋊ C4 |
| Sylow | C73 ⋊ #11260 |
590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=e,c^2=d,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^27,c^b=cf,g^b=gh,g^c=gh,i^g=i^72772 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1093057);