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C₂×#43112 #7667377

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

Aliases

Subgroups

9038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574573);