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C₂×#23108 #6382186

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

Aliases

Subgroups

2944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6289382);