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C₂²×#2814 #7633374

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

Aliases

Subgroups

9982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540570);