Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C163 ⋊ C4×C4⋊Q8 |
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20864 |
Polycyclic presentation:
2^7,163|a^2=g,b^2=e,c^2=f,d^2=eg,b^a=be,c^a=cf,h^c=h^162,h^d=h^1622324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 7079);