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C₂×#13027 #494538

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

Aliases

Subgroups

1346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401734);