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C₂×#39786 #7637413

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

Aliases

Subgroups

6748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544609);