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C₂×#35240 #7628489

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

Aliases

Subgroups

10554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535685);