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C₂×#11041 #357545

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

Aliases

Subgroups

4682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264741);