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C₂²×#2696 #7633425

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

Aliases

Subgroups

12262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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, 7540621);