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C₂×#42931 #7641568

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

Aliases

Subgroups

6390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548764);