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C₂²×#2331 #7625301

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

Aliases

Subgroups

9226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532497);