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C₂×#23509 #6431896

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

Aliases

Subgroups

5606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6339092);