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C₂×#53174 #8105662

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

Aliases

Subgroups

6720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8012858);