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C₂×#7495 #151817

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

Aliases

Subgroups

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 59013);