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C₂×#37334 #7634662

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

Aliases

Subgroups

7604 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)(13,18)(14,16)(15,17)(20,24)(22,25);(4,7)(8,10)(12,14)(17,18)(20,24)(21,26);(3,4)(5,8)(6,7)(9,10)(11,13,16,15)(12,17,14,18)(19,20)(21,25)(22,26)(23,24);(3,4)(5,8)(6,7)(9,10)(11,14,16,12)(13,18,15,17)(19,21,23,26)(20,25,24,22);(3,5,6,9)(4,8,7,10)(11,15,16,13)(12,18,14,17)(19,22,23,25)(20,26,24,21)

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, 7541858);