Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #478×C73 ⋊ C4 |
| Sylow | C73 ⋊ #21619 |
868 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=e,d^2=eg,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^46,d^b=dh,f^c=fh,i^d=i^27,i^g=i^72406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1106874);