Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #17651 |
1060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=f,c^2=g,d^2=gh,e^2=h,f^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eh,f^b=fgh,i^b=i^783184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 137542);