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C₂×#35787 #7629420

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

Aliases

Subgroups

8882 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)(9,10)(11,13)(12,14)(16,20)(17,22);(7,9,12,11)(8,13,14,10)(15,16,19,20)(17,21,22,18);(3,4)(5,6)(7,10)(8,11)(9,14)(12,13)(15,17)(16,21)(18,20)(19,22);(7,10)(8,9)(11,14)(12,13)(15,18,19,21)(16,17,20,22);(7,11,12,9)(8,13,14,10)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536616);