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C₂×#23429 #6431755

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

Aliases

Subgroups

7606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338951);