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C₂²×#3188 #10575394

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

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, 10482590);