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C₂²×#2564 #7627997

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

Aliases

Subgroups

12962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535193);