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C₂²×#2858 #7633332

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

Aliases

Subgroups

17522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(6,7)(10,11)(15,18)(16,20);(5,6,8,7)(9,10,12,11)(13,14,17,19)(15,16,18,20);(9,10,12,11)(13,15,17,18)(14,16,19,20);(5,7,8,6)(9,11,12,10)(13,16)(14,18)(15,19)(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, 7540528);