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C₂×#62257 #10577540

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

Aliases

Subgroups

7210 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)(11,12)(13,20)(14,18)(15,24)(16,19)(17,23)(21,26)(22,25);(3,5)(4,7)(6,10)(8,9)(13,21)(17,25)(20,26)(22,23);(11,13,14,22,16,21,15,23)(12,17,24,26,19,25,18,20);(5,10)(7,9);(4,8)(7,9)(11,14,16,15)(12,18,19,24)(13,22,21,23)(17,20,25,26)

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, 10484736);