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C₂×#26268 #6444506

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

Aliases

Subgroups

2834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351702);