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C₂×#20723 #6370936

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

Aliases

Subgroups

4670 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)(13,16)(14,21,22,17)(15,18)(19,25,26,23)(20,24);(4,7)(8,10)(11,13,15,20)(12,16,18,24)(14,19,22,26)(17,23,21,25);(11,14)(12,17)(13,19)(15,22)(16,23)(18,21)(20,26)(24,25);(3,5,6,9)(4,8,7,10)

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, 6278132);