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C₂×#14321 #515152

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

Aliases

Subgroups

7430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422348);