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C₂²×#2475 #7627883

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

Aliases

Subgroups

9722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535079);