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C₂×#20867 #6371302

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

Aliases

Subgroups

4550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,8,13,9,12,7,23)(5,14,16,10,18,26,17,25)(6,19,21,11,22,28,20,27)(15,30,31,29,32,24,33,34);(3,5,8,16,9,18,7,17)(4,10,13,26,12,25,23,14)(6,15,21,31,22,32,20,33)(11,24,28,34,27,30,19,29);(3,6)(4,11)(5,15)(7,20)(8,21)(9,22)(10,24)(12,27)(13,28)(14,29)(16,31)(17,33)(18,32)(19,23)(25,30)(26,34);(4,12)(10,25)(11,27)(13,23)(14,26)(19,28)(24,30)(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, 6278498);