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C₂×#42074 #7640326

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

Aliases

Subgroups

6760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547522);