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C₂×#42229 #7640579

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

Aliases

Subgroups

5516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547775);