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C₂×#10787 #353469

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

Aliases

Subgroups

4022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 260665);