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C₂×#11522 #480313

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

Aliases

Subgroups

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387509);