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C₂×#2566 #34891

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

Aliases

Subgroups

1547 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27879);