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C₂×#39198 #7637041

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

Aliases

Subgroups

7658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(7,8)(9,10)(11,12,15,18)(13,14,17,16);(4,8)(6,9)(13,17)(14,16)(19,20,22,24)(21,25,26,23);(11,13,15,17)(12,16,18,14)(19,20)(21,23)(22,24)(25,26);(3,5)(4,9)(6,8)(7,10);(3,6,7,9)(4,5,8,10)(11,14,15,16)(12,17,18,13)(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, 7544237);