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C₂×#45220 #7669654

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

Aliases

Subgroups

5858 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)(11,12)(13,14)(15,16)(17,18)(19,20)(21,26)(22,24)(23,25);(3,4)(5,7)(6,9)(8,10)(12,16)(14,17)(19,21,23,22)(20,24,25,26);(4,5)(8,9)(11,13)(12,17)(14,16)(15,18)(19,22,23,21)(20,24,25,26);(3,5,7,4)(6,9,10,8)(11,14,15,17)(12,13,16,18)(19,20)(21,26)(22,24)(23,25);(3,6,7,10)(4,8,5,9)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576850);