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C₂×#27661 #6457143

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

Aliases

Subgroups

2694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6364339);