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C₂×#33552 #7622863

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

Aliases

Subgroups

3878 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)(7,11)(8,12)(9,16)(14,26)(15,27)(17,23)(18,24)(19,32)(20,25)(21,29)(22,30)(28,34)(31,33);(3,5)(4,9)(6,14)(7,16)(8,15)(10,21)(11,13)(12,22)(17,29)(18,28)(19,31)(20,30)(23,26)(24,33)(25,27)(32,34);(3,6,8,18)(4,10,12,24)(5,14,15,28)(7,19,20,17)(9,21,22,33)(11,23,25,32)(13,26,27,34)(16,31,30,29);(5,15)(9,22)(13,27)(14,28)(16,30)(21,33)(26,34)(29,31)

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, 7530059);