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C₂²×#1773 #6369904

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

Aliases

Subgroups

3266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277100);