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C₂²×#1827 #6370892

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

Aliases

Subgroups

4678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278088);