Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C67×#2060 ⋊ C2 |
| Sylow | C67 ⋊ #24323 |
1004 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=eh,b^2=e,c^2=h,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,g^b=gh,f^c=fh,g^c=gh,i^c=i^66,i^d=i^66901 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 205893);