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C₂×#60963 #10575804

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

Aliases

Subgroups

6588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483000);