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C₂×#59318 #7666133

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

Aliases

Subgroups

9044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573329);