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C₂×#34226 #7625512

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

Aliases

Subgroups

9814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532708);