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C₂×#13036 #494555

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

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, 401751);