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C₂×#61758 #10577930

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

Aliases

Subgroups

6532 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)(21,26)(22,31)(23,28)(24,33)(25,29)(27,32)(30,34);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21,25,22)(20,26,29,31)(23,32,24,30)(27,33,34,28);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(19,22,25,21)(20,27,29,34)(23,32,24,30)(26,33,31,28);(5,13)(8,11)(12,18)(15,17);(4,10)(8,11)(9,16)(15,17)(19,23,25,24)(20,28,29,33)(21,30,22,32)(26,34,31,27)

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, 10485126);