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C₂×#47059 #7701120

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

Aliases

Subgroups

5624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7608316);