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C₂×#33571 #7622901

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

Aliases

Subgroups

3669 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530097);