Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #26029 |
658 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=h,c^2=f,d^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,i^b=i^78,g^c=gh,i^d=i^781534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 227751);