Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C71×#1664 ⋊ C2 |
| Sylow | C71 ⋊ #19029 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=h,c^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,d^b=dg,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^c=i^70,i^d=i^70737 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 151128);