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C₂×#23445 #6431792

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

Aliases

Subgroups

8370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338988);