Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C73×#1872 ⋊ C2 |
| Sylow | C73 ⋊ #25584 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=h,b^2=h,c^2=f,d^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^72,c^b=cg,g^b=gh,i^b=i^72,d^c=dh,g^c=gh,i^d=i^721414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 222935);