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C₂×#23019 #6381908

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

Aliases

Subgroups

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289104);