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C₂×#13486 #499357

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

Aliases

Subgroups

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406553);