Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C73×#2097 ⋊ C2 |
| Sylow | C73 ⋊ #23730 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=ef,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,c^b=cg,e^b=eh,f^b=fh,i^b=i^72,e^c=eh,f^c=fh,i^c=i^72,i^d=i^721216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 199367);