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C₂²×#3207 #10575482

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

Aliases

Subgroups

9270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(5,6)(7,11)(8,10)(9,12)(14,17)(15,18)(19,20);(5,7,8,12)(6,9,10,11)(13,14,16,17)(15,19,20,18);(7,12)(9,11)(13,15)(14,18)(16,20)(17,19);(6,10)(9,11)(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, 10482678);