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C₂×#26828 #6443857

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

Aliases

Subgroups

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6351053);