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C₂×#15038 #608120

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

Aliases

Subgroups

3954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515316);