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C₂×#15084 #608203

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515399);