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C₂²×#2472 #7627822

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

Aliases

Subgroups

21126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535018);