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C₂×#20708 #6370893

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

Aliases

Subgroups

4342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,13,15,9)(6,17,19,32)(7,12)(8,11)(10,18,23,33)(14,27)(16,26,30,22)(20,24)(21,29)(25,34)(28,31);(3,5)(4,9)(6,14)(7,16)(8,15)(10,21)(11,13)(12,22)(17,31)(18,29)(19,28)(20,30)(23,25)(24,26)(27,32)(33,34);(3,6)(4,10,11,23)(5,14)(7,18)(8,19)(9,21,13,25)(12,17,24,32)(15,28)(16,29)(20,33)(22,31,26,27)(30,34);(5,15)(9,13)(14,28)(16,30)(21,25)(22,26)(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, 6278089);