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C₂×#15541 #609120

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

Aliases

Subgroups

4746 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)(12,15)(13,17)(19,20,22,23)(21,24,25,26);(8,9)(20,23)(24,26);(7,8,10,9)(11,12)(13,16)(14,15)(17,18)(19,21,22,25)(20,24,23,26);(3,4)(5,6)(7,9,10,8)(11,13,14,17)(12,16,15,18)(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, 516316);