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C₂²×#3522 #10585964

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

Aliases

Subgroups

37458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493160);