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C₂×#20892 #6371340

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

Aliases

Subgroups

4566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278536);