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C₂×#60431 #10574953

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

Aliases

Subgroups

10760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482149);