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C₂×#15567 #609148

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

Aliases

Subgroups

7490 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)(12,14)(15,16)(17,21)(18,19)(20,22);(8,9)(11,12,13,14)(16,19)(17,22);(11,12)(13,14)(15,16)(17,20)(18,19)(21,22);(3,4)(5,6)(7,9,10,8)(11,12)(13,14)(15,17,18,22)(16,20,19,21)

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, 516344);