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C₂×#20776 #6371068

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

Aliases

Subgroups

1990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278264);