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C₂×#59412 #7666191

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

Aliases

Subgroups

14410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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, 7573387);