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C₂×#37171 #7634435

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

Aliases

Subgroups

6364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541631);