Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C163 ⋊ #1828 |
296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2608 |
Polycyclic presentation:
2^7,163|a^2=f,c^2=d,b^a=bd,c^a=ce,d^a=dg,f^b=fg,e^c=eg,h^c=h^1621811 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 4616);