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C₂×#17309 #845283

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

Aliases

Subgroups

4986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 752479);