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C₂²×#2580 #7628057

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

Aliases

Subgroups

12234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535253);