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C₂×#23872 #6437580

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

Aliases

Subgroups

6446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344776);