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C₂×#18530 #6348075

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

Aliases

Subgroups

3150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255271);