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C₂²×C₃×#585 #10681707

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

60366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 23 points:

(1,2)(21,22,23);(3,4);(5,6)(7,13)(8,12)(9,11)(10,14)(15,19)(16,18)(17,20);(5,7)(6,10)(8,15)(9,14)(11,13)(12,17)(16,20)(18,19);(7,14)(10,13)(15,20)(17,19);(6,11)(10,13)(12,18)(17,19);(5,8,9,16)(6,12,11,18)(7,15,14,20)(10,17,13,19)

Conjugacy classes & character table

408 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 56088);