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C₂×#37684 #7634929

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

Aliases

Subgroups

10170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542125);