Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×H(3,ℤ/4)×C67 ⋊ C2 |
| Sylow | C67 ⋊ #10949 |
990 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=g,c^2=ef,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,e^b=eh,f^b=fh,i^b=i^66,d^c=dh,i^c=i^661510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 75965);