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C₂×#62610 #10580030

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

Aliases

Subgroups

6644 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)(21,27)(22,29)(24,30)(26,32)(28,33)(31,34);(3,5)(4,9)(6,13)(7,15)(8,14)(10,17)(11,12)(16,18)(19,20,23,25)(21,24,28,31)(22,26,29,32)(27,30,33,34);(3,6,8,7)(4,10,11,16)(5,13,14,15)(9,17,12,18)(19,21,22,27,23,28,29,33)(20,24,26,30,25,31,32,34);(5,14)(9,12)(13,15)(17,18)(21,28)(24,31)(27,33)(30,34);(3,7,8,6)(4,10,11,16)(5,15,14,13)(9,17,12,18)(20,25)(21,28)(26,32)(27,33)

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, 10487226);