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C₂×#35305 #7628586

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

Aliases

Subgroups

23894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535782);