Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2179 ⋊ C2 |
| Sylow | C79 ⋊ #33854 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^78,d^b=de,e^b=eg,g^b=gh,f^c=fh,i^c=i^78,e^d=eg,g^d=gh1285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 326316);