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C₂×#62602 #10580021

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

Aliases

Subgroups

6450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10487217);