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C₂²×#2552 #7628099

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

Aliases

Subgroups

8762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535295);