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C₂²×#2819 #7633389

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

Aliases

Subgroups

12826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540585);