Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C67×#1942 ⋊ C2 |
| Sylow | C67 ⋊ #13474 |
382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=de,b^2=dg,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,c^b=cf,i^b=i^66,d^c=dg,e^c=egh,f^c=fgh,g^c=gh,i^c=i^661504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 89318);