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C₂×#2552 #34931

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

Aliases

Subgroups

1223 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27919);