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C₂×#13269 #495340

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

Aliases

Subgroups

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402536);