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C₂×#23971 #6451792

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

Aliases

Subgroups

4252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6358988);