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C₂×#36708 #7634117

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

Aliases

Subgroups

8594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(9,13)(12,14)(15,16,20,23)(17,18,25,21)(19,27,28,22)(24,29,30,26);(8,11)(12,14)(15,17,20,25)(16,21,23,18)(19,24,28,30)(22,29,27,26);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14);(7,8)(9,12)(10,11)(13,14)(15,18,20,21)(16,17,23,25)(19,26,28,29)(22,24,27,30);(7,9)(8,12)(10,13)(11,14)(15,19)(16,22)(17,24)(18,26)(20,28)(21,29)(23,27)(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, 7541313);