Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #419×C73 ⋊ C4 |
| Sylow | C73 ⋊ #20417 |
1522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=fh,d^2=h,e^2=h,g^2=h,b^a=be,e^a=eh,g^a=gh,i^a=i^46,i^b=i^46,d^c=dh,i^c=i^27,i^f=i^72,i^g=i^72484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1103705);