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C₂²×#2681 #7633436

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

Aliases

Subgroups

14022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540632);