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C₂×#34919 #7628086

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

Aliases

Subgroups

8530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535282);