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C₂×#62331 #10577622

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

Aliases

Subgroups

6814 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)(13,21)(15,17)(19,22)(23,24)(25,26);(3,5)(4,7)(6,10)(8,9)(11,12,16,18)(13,19,24,25)(14,17,20,15)(21,26,23,22);(11,13,17,21,16,24,15,23)(12,19,20,26,18,25,14,22);(5,10)(7,9)(11,14,16,20)(12,15,18,17)(13,22,24,26)(19,23,25,21);(4,8)(7,9)(11,15,16,17)(12,20,18,14)(13,23,24,21)(19,26,25,22)

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, 10484818);