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C₂×#28502 #6465670

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

Aliases

Subgroups

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6372866);