Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C73×#1524 ⋊ C2 |
| Sylow | C73 ⋊ #8402 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=g,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eg,f^b=fgh,d^c=dg,f^c=fg,i^c=i^721414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 61363);