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C₃⋊((C₃⋊D₃)⋊C₉) #92291

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 21 points:

(2,3)(4,8,12,6,11,7,9,5,10)(14,19,21,16,17,20)(15,18);(1,2,3);(13,14,16)(15,17,20)(18,21,19)

Polycyclic presentation:

2,3^5|b^3=c,d^a=d^2,e^a=e^2,f^a=f^2,d^b=df

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 136);