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C₂×#20584 #6370688

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

Aliases

Subgroups

18642 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)(9,15,17,12)(10,13)(11,14)(16,21,22,19)(18,20);(7,9)(8,12)(10,16)(11,17)(13,19)(14,15)(18,22)(20,21);(4,6);(7,10,11,18)(8,13,14,20)(9,16,17,22)(12,19,15,21)

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, 6277884);