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C₂×#15386 #608920

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

Aliases

Subgroups

4778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516116);