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C₂×#25899 #6446738

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

Aliases

Subgroups

5416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6353934);