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C₂×#13032 #494549

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

Aliases

Subgroups

1338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401745);