Finite Group Databasebeta

?

← Prev (#6448876) Next (#6448878) →

C₂×#24643 #6448877

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

Aliases

Subgroups

2624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6356073);