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C₂²×#2674 #7633453

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

Aliases

Subgroups

12454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540649);