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C₂²×#2686 #7633430

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

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, 7540626);