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C₂×#13068 #494649

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

Aliases

Subgroups

1322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401845);