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C₂×#21784 #6374201

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

Aliases

Subgroups

4386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281397);