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C₂×#62342 #10577635

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

Aliases

Subgroups

7062 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)(19,22)(21,25)(23,24);(3,5)(4,7)(6,10)(8,9)(11,12)(13,21)(14,17)(15,26)(16,18)(19,24)(20,22)(23,25);(11,13,17,20,16,24,15,23)(12,19,14,25,18,21,26,22);(5,10)(7,9)(11,14)(12,15)(13,22)(16,26)(17,18)(19,20)(21,23)(24,25);(4,8)(7,9)(11,15,16,17)(12,14,18,26)(13,23,24,20)(19,25,21,22)

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, 10484831);