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C₂×#23798 #6432586

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

Aliases

Subgroups

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339782);