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C₂×#59117 #7666596

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

Aliases

Subgroups

9418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573792);