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C₂²×#2670 #7633451

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

Aliases

Subgroups

21370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540647);