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C₂×#62328 #10577618

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

Aliases

Subgroups

7310 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)(12,18)(13,20)(15,17)(19,26)(21,25)(22,23);(3,5)(4,7)(6,10)(8,9)(11,12)(13,19)(14,17)(15,24)(16,18)(20,21)(22,26)(23,25);(11,13,15,22,16,23,17,20)(12,19,24,26,18,25,14,21);(5,10)(7,9)(11,14)(12,15)(13,21)(16,24)(17,18)(19,22)(20,25)(23,26);(4,8)(7,9)(11,15,16,17)(12,14,18,24)(13,22,23,20)(19,21,25,26)

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, 10484814);