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Aliases
Splittings
Subgroups
50 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
2^4,3^2,5|b^2=c,c^2=d,b^a=bc,c^a=cd,e^a=ef,f^a=f^2,g^a=g^4,e^b=ef^2,f^b=e^2,e^c=e^2f^2,f^c=e^2f,e^d=e^2,f^d=f^2
Conjugacy classes & character table
27 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | D5×AΓL(1,𝔽9), C2×AGL(1,𝔽9)⋊D5, C3×AGL(1,𝔽9)⋊D5 |
| maximal normal subgroup of | D5×AΓL(1,𝔽9), C2×AGL(1,𝔽9)⋊D5, C3×AGL(1,𝔽9)⋊D5 |
| maximal quotient of | #13088399, #13088400, AGL(1,𝔽9)⋊Dic5, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 782);
Finite Group Databasebeta