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C₂×#21337 #6372231

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

Aliases

Subgroups

3646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279427);