Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C73×#1309 ⋊ C2 |
| Sylow | C73 ⋊ #8128 |
566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=g,e^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fh,d^b=dh,e^b=eg,i^c=i^72988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 59982);