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C₂×#62829 #10586177

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

Aliases

Subgroups

32360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493373);