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C₂×#21304 #6372171

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

Aliases

Subgroups

3778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279367);