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C₂²×#2956 #10574144

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

Aliases

Subgroups

10430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481340);