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C₂×#25768 #6443151

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

Aliases

Subgroups

5716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

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, 6350347);