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C₂×#10794 #353382

• 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);(3,4,7,14,9,12,8,13)(5,10,17,25,16,26,22,24)(6,18,21,27,19,28,20,11)(15,29,31,34,32,33,30,23);(3,5,8,17,9,16,7,22)(4,10,14,24,12,26,13,25)(6,15,20,31,19,32,21,30)(11,23,18,33,27,34,28,29);(3,6)(4,11)(5,15)(7,21)(8,20)(9,19)(10,23)(12,27)(13,28)(14,18)(16,32)(17,31)(22,30)(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, 260578);