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C₂×#12809 #493739

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

Aliases

Subgroups

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400935);