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C₂×#41995 #7640506

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

Aliases

Subgroups

8350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7547702);