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C₂×#33427 #7622561

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

Aliases

Subgroups

1506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 7529757);