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C₂×#52004 #7708049

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

Aliases

Subgroups

13562 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);(8,12)(9,13)(15,16)(17,19)(18,21)(20,22);(3,4)(5,6)(16,17)(20,21);(7,9,11,13)(8,10,12,14)(15,17,19,16)(18,21,22,20);(7,10)(8,13)(9,12)(11,14)(15,18,19,22)(16,20,17,21)

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, 7615245);