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C₂×#21969 #6374924

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

Aliases

Subgroups

2150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12,15,18,16,19,14,24)(13,20,22,25,23,26,21,17);(3,5,6,10)(4,7,8,9);(5,10)(7,9)(11,13,14,21,16,23,15,22)(12,17,18,20,19,25,24,26);(4,8)(7,9)

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, 6282120);