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C₂×#41409 #7639828

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

Aliases

Subgroups

8904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547024);