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C₂²×#3253 #10575602

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

Aliases

Subgroups

9142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482798);