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C₂×#60892 #10575735

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

Aliases

Subgroups

6358 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)(21,30)(22,33)(23,28)(24,26)(25,31)(27,34)(29,32);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(19,21,23,31)(20,25,28,30)(22,32,34,24)(26,27,29,33);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17)(20,26)(21,31)(24,32)(25,33)(27,30)(28,29);(4,10)(8,11)(9,18)(16,17)(19,22)(20,27)(21,32)(23,34)(24,31)(25,29)(26,30)(28,33);(21,31)(22,34)(25,30)(27,33)

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, 10482931);