Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C67×#1306 ⋊ C2 |
| Sylow | C67 ⋊ #8752 |
754 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 87 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,c^2=dh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,i^b=i^66,e^c=eg,f^c=fh892 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 63086);