Finite Group Databasebeta

?

← Prev (#7623022) Next (#7623024) →

C₂²×#2231 #7623023

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

Aliases

Subgroups

1506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(1,2);(3,4);(5,6,11,16)(7,17,20,15)(8,21)(9,25,18,14)(10,12,27,29)(13,30)(19,33)(22,35)(23,34)(24,28)(26,31)(32,36);(5,7,18,27,11,20,9,10)(6,12,25,15,16,29,14,17)(8,19,23,36,24,30,22,26)(13,28,32,34,33,21,31,35);(5,8)(6,13)(7,19)(9,22)(10,26)(11,24)(12,28)(14,31)(15,34)(16,33)(17,35)(18,23)(20,30)(21,29)(25,32)(27,36)

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, 7530219);