Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C73×#1947 ⋊ C2 |
| Sylow | C73 ⋊ #10587 |
454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=de,b^2=d,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,i^b=i^72,d^c=dg,e^c=eh,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, 74082);