Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2263 ⋊ C2 |
| Sylow | C79 ⋊ #33981 |
466 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=be,c^a=ch,e^a=ef,f^a=fg,g^a=gh,e^b=ef,f^b=fg,g^b=gh,i^d=i^781066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 327710);