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C₂×#23907 #6437432

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

Aliases

Subgroups

7070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344628);