Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C73 ⋊ #17986 |
578 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=fg,d^2=g,e^2=g,f^2=h,b^a=be,c^a=ch,d^a=dgh,e^a=eg,i^a=i^46,d^b=dh,e^b=eg,i^c=i^27,i^f=i^72340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1102628);