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C₂×#27279 #6440749

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

Aliases

Subgroups

3860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6347945);