Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C67×#3271 ⋊ C2 |
| Sylow | C67 ⋊ #61096 |
2686 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=h,d^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^66,d^b=df,e^b=eh,f^b=fh,i^b=i^66,e^c=eh,f^d=fh,i^d=i^66,i^e=i^661012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 1045723);