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C₂²×#2140 #7622490

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

Aliases

Subgroups

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2);(3,4);(5,6,7,8)(9,10)(11,16)(12,15)(13,22)(14,18)(17,20)(19,23)(21,24);(10,15)(11,13)(12,20)(16,17)(18,24)(19,21)(22,23);(9,11,14,13)(10,16,18,22)(12,19,21,20)(15,23,24,17)

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, 7529686);