Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #7278 |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,i^a=i^72,c^b=cg,d^b=dh,i^b=i^722062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 56767);