Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C79×#2122 ⋊ C2 |
| Sylow | C79 ⋊ #33559 |
1248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^8,79|d^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^78,d^b=dh,f^b=fgh,d^c=dh,e^c=eg,i^c=i^78,f^e=fh931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 323701);