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C₂²×#1876 #6371393

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

Aliases

Subgroups

6354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6278589);