Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×#1823 ⋊ C2 |
| Sylow | C73 ⋊ #9470 |
598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=dfgh,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,e^b=eh,d^c=dh,f^c=fh,i^c=i^721417 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 67339);