Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×SD16⋊C8 ⋊ C2 |
| Sylow | C79 ⋊ C8×#137 |
714 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=f,e^2=g,f^2=h,b^a=be,d^a=dg,e^a=eg,i^a=i^78,e^b=eg,i^c=i^78,i^d=i^781804 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 138996);