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C₉⋊(C₂²⋊C₉) #66356

• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 22 points:

(1,4)(2,3)(14,15,18,16,17,21,19,20,22);(2,3,4)(5,6,8,7,9,11,10,12,13)(15,17,20)(18,22,21)

Polycyclic presentation:

3^4,2^2|a^3=c,b^3=d,b^a=bd,e^a=f,f^a=ef

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 48);