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C₂×#42742 #7641205

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

Aliases

Subgroups

5586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7548401);