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C₂×#45688 #7702083

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

Aliases

Subgroups

6090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609279);