Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C67 ⋊ #8780 |
310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=e,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,f^b=fg,i^b=i^66,f^c=fg1516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 63212);