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C₂×#31142 #7503517

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

Aliases

Subgroups

2660 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)(9,11)(10,12)(13,14)(16,19)(20,22);(7,9,11,8)(10,13,14,12)(16,20)(18,21)(19,22);(4,6)(7,10,11,14)(8,12,9,13)(15,16,17,19)(18,22,21,20);(4,6)(8,9)(12,13)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7410713);