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C₂×#39434 #7636643

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

Aliases

Subgroups

10388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543839);