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C₂×#62504 #10579790

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

Aliases

Subgroups

6204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10486986);