Finite Group Databasebeta

?

← Prev (#6464054) Next (#6464056) →

C₂×#28651 #6464055

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

Aliases

Subgroups

2142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6371251);