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C₂×#25714 #6450125

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

Aliases

Subgroups

3624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6357321);