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C₂×#59281 #7666355

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

Aliases

Subgroups

6406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573551);