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C₂×#40591 #7639023

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

Aliases

Subgroups

8430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546219);