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C₂×#39326 #7636930

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

Aliases

Subgroups

6546 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)(13,17)(14,16)(15,18);(3,4,7,5)(6,9,10,8)(11,12,14,16)(13,15,18,17)(19,20,22,24)(21,25,26,23);(11,13)(12,15)(14,18)(16,17)(19,20)(21,23)(22,24)(25,26);(3,5,7,4)(6,9,10,8)(11,13)(12,15)(14,18)(16,17);(3,6,7,10)(4,8,5,9)(11,12)(13,15)(14,16)(17,18)(19,21,22,26)(20,23,24,25)

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, 7544126);