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C₂×#62823 #10586171

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

Aliases

Subgroups

32030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,9,10)(5,13,14,11)(6,16,15,12)(7,8,17,18)(20,24)(22,29)(25,30)(28,33);(4,10)(5,14)(7,17)(12,16)(21,27)(25,30)(28,33)(32,34);(3,5,9,14)(4,11,10,13)(6,7,15,17)(8,16,18,12)(19,20,23,24)(21,25,27,30)(22,26,29,31)(28,32,33,34);(3,6,9,15)(4,12,10,16)(5,7,14,17)(8,13,18,11);(3,7)(4,8)(5,15)(6,14)(9,17)(10,18)(11,16)(12,13)(19,21)(20,25)(22,28)(23,27)(24,30)(26,32)(29,33)(31,34);(3,8)(4,7)(5,16)(6,13)(9,18)(10,17)(11,15)(12,14)(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, 10493367);