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C₂×#37866 #7635292

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

Aliases

Subgroups

8194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542488);