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C₂×#20838 #6371255

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

Aliases

Subgroups

5018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,6)(7,8)(9,10)(11,12,16,13,15,18,23,20)(14,17,22,19,21,24,26,25);(4,6)(11,13,16,18,15,20,23,12)(14,19,22,24,21,25,26,17);(8,10)(11,14)(12,17)(13,19)(15,21)(16,22)(18,24)(20,25)(23,26);(14,21)(17,24)(19,25)(22,26)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278451);