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C₂²×#1992 #6372199

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

Aliases

Subgroups

4250 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)(11,15)(12,13)(14,16)(18,21)(19,23)(22,24);(6,8)(10,13)(14,15)(17,18,19,21,20,22,23,24);(9,11,12,16)(10,14,13,15)(18,22)(21,24)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279395);