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C₂×#61795 #10577971

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

Aliases

Subgroups

6558 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)(19,20)(21,25)(22,27)(23,26)(24,29)(28,31)(30,34)(32,33);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21,24,30)(20,25,29,34)(22,31,32,23)(26,27,28,33);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(20,26)(21,30)(23,31)(25,33)(27,34)(28,29);(5,13)(8,11)(12,18)(15,17)(19,22)(20,27)(21,31)(23,30)(24,32)(25,28)(26,34)(29,33);(4,10)(8,11)(9,16)(15,17)(21,30)(22,32)(25,34)(27,33)

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, 10485167);