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C₂×#53116 #8092835

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

Aliases

Subgroups

7592 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)(13,17)(15,18)(19,20,23,21)(22,25,26,24);(11,12)(13,15)(14,16)(17,18)(20,21)(22,26);(4,5)(8,9)(11,12,14,16)(13,15,17,18)(19,21,23,20)(22,25,26,24);(3,5,7,4)(6,9,10,8)(11,12)(13,15)(14,16)(17,18)(19,22)(20,24)(21,25)(23,26);(3,6,7,10)(4,8,5,9)(11,13,14,17)(12,15,16,18)

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, 8000031);