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C₂×#25679 #6450043

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

Aliases

Subgroups

3598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6357239);