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C₂²×#2341 #7625346

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

Aliases

Subgroups

25730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532542);