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C₂×#26977 #6443635

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

Aliases

Subgroups

3078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350831);