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C₂×#34129 #7625358

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

Aliases

Subgroups

9470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532554);