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C₂×#21393 #6372387

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

Aliases

Subgroups

4870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279583);