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C₂×#35152 #7628374

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

Aliases

Subgroups

11134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535570);