Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M32×C73 ⋊ C4 |
| Sylow | C73 ⋊ #12561 |
570 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,d^2=gh,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,i^a=i^27,c^b=ch,i^e=i^72784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1095762);