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C₂×#23734 #6432410

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

Aliases

Subgroups

3874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339606);