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C₂²×#1914 #6371553

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

Aliases

Subgroups

6826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278749);