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C₂²×#2122 #7622443

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

Aliases

Subgroups

4982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529639);