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C₂×#39745 #7637429

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

Aliases

Subgroups

10430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544625);