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C₂×#43117 #7667374

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

Aliases

Subgroups

9146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574570);