Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C73×#2241 ⋊ C2 |
| Sylow | C73 ⋊ #33707 |
622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|b^2=f,c^2=e,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,i^a=i^72,d^b=dh,d^c=dh,i^d=i^721420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 324941);