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C₂×#23856 #6437491

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

Aliases

Subgroups

6250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344687);