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C₂×#39437 #7636673

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

Aliases

Subgroups

8400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543869);