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×#106×C79 ⋊ C2 |
| Sylow | C79 ⋊ #20454 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=ef,e^2=h,f^2=h,b^a=be,d^a=dh,e^b=eh,f^b=fh,d^c=dh,i^d=i^782272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 167648);