Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #585×C73 ⋊ C4 |
| Sylow | C73 ⋊ #20615 |
3718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^27,e^b=eh,f^b=fh,e^c=eh,i^g=i^72676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1104467);