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C₂×#62286 #10577586

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

Aliases

Subgroups

6942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10484782);