Finite Group Databasebeta

?

← Prev (#6437947) Next (#6437949) →

C₂×#24473 #6437948

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

Aliases

Subgroups

4537 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345144);