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C₂×#13158 #494935

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

Aliases

Subgroups

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402131);