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C₂×#41413 #7639868

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

Aliases

Subgroups

8658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(8,11)(9,13)(15,16,20,24)(17,25,26,21)(18,22,28,30)(19,23,29,27);(7,8,10,11)(9,12,13,14)(17,26)(19,29)(21,25)(23,27);(3,4,5,6)(7,8)(9,12)(10,11)(13,14)(15,17,20,26)(16,21,24,25)(18,27,28,23)(19,22,29,30);(7,9,10,13)(8,12,11,14)(15,18)(16,22)(17,23)(19,21)(20,28)(24,30)(25,29)(26,27);(15,19)(16,23)(17,22)(18,21)(20,29)(24,27)(25,28)(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, 7547064);