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C₂×#61166 #10576337

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

Aliases

Subgroups

8100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483533);