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C₂×#23181 #6382742

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

Aliases

Subgroups

2732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289938);