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C₂×#23862 #6437506

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

Aliases

Subgroups

6878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344702);