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C₂×#2702 #52123

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

Aliases

Subgroups

1393 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(8,11)(12,13)(15,16,18,20)(17,21,22,19);(4,6)(7,8,10,11)(9,13,14,12)(15,16,18,20)(17,19,22,21);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16)(17,19)(18,20)(21,22);(7,9,10,14)(8,12,11,13)(15,17)(16,19)(18,22)(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, 45111);