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C₂×#47143 #7701060

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

Aliases

Subgroups

5586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7608256);