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C₂×#10740 #353418

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

Aliases

Subgroups

4994 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)(9,15)(10,18)(11,14)(12,16)(13,19)(17,21)(20,22);(7,9)(8,12,14,20)(10,16)(11,17)(13,15,18,21)(19,22);(10,19)(13,18)(15,21)(16,22)

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, 260614);