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C₂²×#1996 #6372222

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

Aliases

Subgroups

5922 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)(8,9)(10,12)(13,14)(15,17,19,20)(16,18);(6,9)(10,11)(13,15)(14,17,18,20)(16,19);(5,7,8,12)(6,10,9,11)

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, 6279418);