Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2956 ⋊ C2 |
| Sylow | C79 ⋊ #22899 |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^8,79|a^2=g,b^2=g,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=de,e^b=eh,d^c=dh,f^c=fh,i^c=i^78,e^d=eh1774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 190440);