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C₃²×#1437 #11768486

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 22 points:

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

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2497);