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C₂×#60312 #10574472

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

Aliases

Subgroups

6906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481668);