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C₂×#2690 #52110

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

Aliases

Subgroups

1263 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45098);