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C₂×#21777 #6374185

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

Aliases

Subgroups

4496 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)(6,10)(7,19,20,11)(8,12)(14,21,28,23)(15,22)(17,30,31,24)(18,25)(26,29)(27,33)(32,34);(3,5)(4,9)(6,14)(7,15)(8,16)(10,23)(11,22)(12,13)(17,27)(18,28)(19,26)(20,29)(21,25)(24,33)(30,32)(31,34);(3,6,8,18)(4,10,12,25)(5,14,16,28)(7,17,20,31)(9,21,13,23)(11,24,19,30)(15,27,29,34)(22,32,26,33);(3,7)(4,11)(5,15)(6,17)(8,20)(9,22)(10,24)(12,19)(13,26)(14,27)(16,29)(18,31)(21,32)(23,33)(25,30)(28,34)

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, 6281381);