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C₂×#35242 #7628498

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

Aliases

Subgroups

23334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535694);