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C₂×#60141 #10574195

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

Aliases

Subgroups

11146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481391);