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C₂²×#2186 #7622804

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

Aliases

Subgroups

4190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530000);