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C₂×#33689 #7623145

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

Aliases

Subgroups

1489 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530341);