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C₂²×#2213 #7622947

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

Aliases

Subgroups

2390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530143);