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C₂×#52166 #7633498

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

Aliases

Subgroups

7688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540694);