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C₂×#40603 #7639485

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

Aliases

Subgroups

8668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546681);