Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#405×C79 ⋊ C2 |
| Sylow | C79 ⋊ #60167 |
2706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=g,c^2=g,e^2=h,f^2=h,b^a=bf,d^a=dh,f^a=fh,i^a=i^78,f^b=fh,i^b=i^78,d^c=dh3208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1033745);