Finite Group DatabasebetaFinite Group Databasebeta| order | 20288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #101×C317 ⋊ C2 |
| Sylow | C317 ⋊ #355 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5072 |
Polycyclic presentation:
2^6,317|a^2=d,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^316,d^c=df1751 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20288, 345);