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C₂×#37786 #7635063

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

Aliases

Subgroups

9456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542259);