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C₂×#41974 #7640320

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

Aliases

Subgroups

6126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547516);