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C₂×#62336 #10577628

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

Aliases

Subgroups

6926 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)(21,22)(23,24);(3,5)(4,7)(6,10)(8,9)(11,12)(13,21)(14,17)(15,25)(16,18)(19,24)(20,26)(22,23);(11,13,17,20,16,24,15,23)(12,19,14,22,18,21,25,26);(5,10)(7,9)(11,14)(12,15)(13,22)(16,25)(17,18)(19,23)(20,21)(24,26);(4,8)(7,9)(11,15,16,17)(12,14,18,25)(13,23,24,20)(19,22,21,26)

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, 10484824);