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C₂²×#2022 #6431789

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

Aliases

Subgroups

8902 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)(9,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,23)(22,24);(9,11,13,18)(10,14,16,21)(12,17,19,24)(15,22,23,20);(6,8)(9,12)(10,15)(11,17)(13,19)(14,20)(16,23)(18,24)(21,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338985);