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C₂×#51785 #7707791

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

Aliases

Subgroups

9382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7614987);