Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #9723 |
422 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=df,c^2=e,d^2=gh,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^66,d^b=dh,f^b=fh,i^b=i^66,i^c=i^661312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 68754);