Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #7274 |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,c^2=fh,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,c^b=cg,i^b=i^27,i^e=i^72562 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1084177);