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C₂×#25772 #6443346

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

Aliases

Subgroups

5488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350542);