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C₂×#62252 #10577534

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

Aliases

Subgroups

6864 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)(11,12,16,19)(13,20,23,26)(14,18,15,24)(17,21,25,22);(3,5)(4,7)(6,10)(8,9);(11,13,14,21,16,23,15,22)(12,17,24,26,19,25,18,20);(5,10)(7,9);(4,8)(7,9)(11,14,16,15)(12,18,19,24)(13,21,23,22)(17,20,25,26)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484730);