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C₂²×#3138 #10575200

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

Aliases

Subgroups

10858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482396);