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C₂×#15634 #609252

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

Aliases

Subgroups

6966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516448);