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C₂×#23895 #6437626

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

Aliases

Subgroups

7222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344822);