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C₂×#20860 #6371291

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

Aliases

Subgroups

4510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278487);