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C₂²×#2551 #7628092

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

Aliases

Subgroups

12106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

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, 7535288);