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C₂×#26058 #6443372

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

Aliases

Subgroups

2560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350568);