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C₂×#20675 #6370828

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

Aliases

Subgroups

4542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278024);