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C₂×#39596 #7637266

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

Aliases

Subgroups

8594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544462);