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C₂×#36718 #7634061

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

Aliases

Subgroups

10662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541257);