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C₂×#37614 #7633884

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

Aliases

Subgroups

12470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541080);