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C₂²×#2506 #7627926

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

Aliases

Subgroups

8458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535122);