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C₂²×#3247 #10575596

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

Aliases

Subgroups

8198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482792);