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C₂×#61778 #10577952

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

Aliases

Subgroups

6574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10485148);