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C₂×#13442 #499177

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

Aliases

Subgroups

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406373);