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C₂×#15765 #609441

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

Aliases

Subgroups

5046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,10,9)(11,12,14,13)(17,21)(19,22);(8,9)(12,13)(15,16,18,20)(17,19,21,22);(11,12,14,13)(15,17)(16,19)(18,21)(20,22);(3,4)(5,6)(7,9,10,8)(11,13,14,12)(15,17)(16,19)(18,21)(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, 516637);