Finite Group Databasebeta

?

← Prev (#7504662) Next (#7504664) →

C₂×#31416 #7504663

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

Aliases

Subgroups

1917 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,9,14)(5,15,18,10)(6,20,23,32)(7,13,8,12)(11,25,30,22)(16,29,34,27)(17,33,21,26)(19,28,24,31);(3,5,7,24,9,18,8,19)(4,10,12,31,14,15,13,28)(6,21,22,34,23,17,25,16)(11,29,20,33,30,27,32,26);(3,6)(4,11)(5,16,18,34)(7,25)(8,22)(9,23)(10,26,15,33)(12,32)(13,20)(14,30)(17,19,21,24)(27,28,29,31);(3,6)(4,11)(5,17)(7,25)(8,22)(9,23)(10,27)(12,32)(13,20)(14,30)(15,29)(16,19)(18,21)(24,34)(26,28)(31,33)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411859);