Finite Group Databasebeta

?

← Prev (#610997) Next (#610999) →

C₂×#16481 #610998

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

Aliases

Subgroups

4782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518194);