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C₂²×#3291 #10576166

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

Aliases

Subgroups

10450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483362);