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C₂×#7162 #126667

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

Aliases

Subgroups

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

(1,2);(3,4,6,13,9,15,24,32,10,16,25,14,8,26,7,12)(5,17,19,30,22,28,34,33,23,31,18,11,21,27,20,29);(3,5,7,20,8,21,25,18,10,23,24,34,9,22,6,19)(4,11,14,28,15,29,12,31,16,30,13,27,26,33,32,17)

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, 33863);