Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×SD32×C73 ⋊ C4 |
| Sylow | C73 ⋊ #33457 |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=h,c^2=f,e^2=gh,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,i^a=i^46,e^b=eg,g^b=gh,d^c=dh,i^c=i^27,i^f=i^72460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113849);