Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×#97×C73 ⋊ C2 |
| Sylow | C73 ⋊ #20512 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,i^a=i^72,e^b=eh,i^b=i^72,d^c=dh2968 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 168154);