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C₂×#37665 #7635026

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

Aliases

Subgroups

9250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542222);