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C₂×#10783 #353463

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

Aliases

Subgroups

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260659);