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C₂×#2726 #52150

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

Aliases

Subgroups

1123 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45138);