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C₂×#20787 #6371100

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

Aliases

Subgroups

1736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278296);