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C₂×#13789 #513404

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

Aliases

Subgroups

5970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420600);