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C₂×#13270 #495342

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

Aliases

Subgroups

804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402538);