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C₂×#37794 #7635016

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

Aliases

Subgroups

8854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542212);