Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#2122 ⋊ C2 |
| Sylow | C79 ⋊ #33348 |
1410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^8,79|a^2=f,b^a=be,e^a=eg,g^a=gh,f^b=fg,i^b=i^78,d^c=dh,i^c=i^78,i^d=i^78,f^e=fh943 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 322318);