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C₂×#61892 #10578565

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

Aliases

Subgroups

6460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10485761);