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C₂×#23361 #6407632

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

Aliases

Subgroups

2206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6314828);