Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C67×#1392 ⋊ C2 |
| Sylow | C67 ⋊ #13052 |
624 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=df,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=egh,g^a=gh,c^b=ch,e^b=egh,i^b=i^66,d^c=dg,e^c=eh,f^c=fg,i^c=i^66,e^d=eh,f^e=fh892 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 86894);