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C₂×#17281 #845146

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

Aliases

Subgroups

3570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 752342);