Finite Group Databasebeta

?

← Prev (#514781) Next (#514783) →

C₂×#14253 #514782

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

Aliases

Subgroups

4118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421978);