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C₂×#21286 #6372106

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

Aliases

Subgroups

2786 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)(9,12)(10,11)(13,14)(16,19)(17,21)(20,22);(3,5,6,4)(8,11)(12,14);(15,16,17,19,18,20,21,22);(7,9,10,13)(8,12,11,14)(16,20)(19,22)

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, 6279302);