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C₂×#11033 #357588

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

Aliases

Subgroups

4366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264784);