Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#2201 ⋊ C2 |
| Sylow | C79 ⋊ #33552 |
1156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|c^2=h,b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,i^b=i^78,e^c=eg,i^c=i^78,i^d=i^78,f^e=fh697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 323639);