Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×#131×C79 ⋊ C2 |
| Sylow | C79 ⋊ #20510 |
1006 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,c^a=ch,e^a=eh,e^b=eh,i^b=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 168129);