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C₂×#17981 #6344846

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

Aliases

Subgroups

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252042);