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C₂×#33347 #7622445

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

Aliases

Subgroups

4294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529641);