Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C163 ⋊ C2 |
| Sylow | C163 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10432 |
Polycyclic presentation:
2^7,163|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^162,d^b=de,e^b=ef,f^b=fg,h^b=h^1623266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 6830);