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C₂²×#3278 #10576049

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

Aliases

Subgroups

10814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483245);