Finite Group DatabasebetaFinite Group Databasebeta| order | 20864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#123×C163 ⋊ C2 |
| Sylow | C163 ⋊ #2418 |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5216 |
Polycyclic presentation:
2^7,163|b^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^162,h^d=h^1622306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20864, 7969);