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C₂²×#2418 #7627812

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

Aliases

Subgroups

21650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(6,8)(14,17)(15,19);(5,6)(7,8)(10,12)(13,14,16,17)(15,18,19,20);(9,10)(11,12)(13,14)(15,18)(16,17)(19,20);(5,6)(7,8)(13,15)(14,18)(16,19)(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, 7535008);