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C₃²×#1438 #11768487

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2498);