Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C163 ⋊ C2 |
| Sylow | C163 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10432 |
Polycyclic presentation:
2^7,163|a^2=g,b^2=f,c^2=f,e^2=g,b^a=bf,d^a=df,c^b=cf,h^c=h^162,h^e=h^1622822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 17721);