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C₂×#24257 #6442633

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

Aliases

Subgroups

5744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349829);