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C₂×#12882 #494067

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

Aliases

Subgroups

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401263);