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C₂×#23859 #6437489

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

Aliases

Subgroups

6336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344685);