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C₂×#33022 #6629254

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

Aliases

Subgroups

5270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536450);