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C₂×#37838 #7635220

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

Aliases

Subgroups

9304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542416);