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C₂×#34191 #7625422

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

Aliases

Subgroups

8990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532618);