Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C67×#1393 ⋊ C2 |
| Sylow | C67 ⋊ #12581 |
854 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 151 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=e,b^2=f,c^2=h,d^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,e^b=egh,i^c=i^66,e^d=eh910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 84536);