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C₂×#3054 #60441

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

Aliases

Subgroups

1459 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53429);