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C₂×#9678 #204494

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

Aliases

Subgroups

2058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(4,6)(8,12,13,14)(15,16,18,21,19,22,17,20);(7,8,9,12,11,13,10,14)(16,20)(17,18)(21,22);(3,4,5,6)(7,9,11,10)(8,12,13,14)(15,17,19,18)(16,20,22,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111690);