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C₂×#62937 #10586280

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

Aliases

Subgroups

32430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493476);