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C₂×#47115 #7700813

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

Aliases

Subgroups

6356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7608009);