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C₂×#15674 #609310

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

Aliases

Subgroups

8034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516506);