Finite Group Databasebeta

?

← Prev (#493242) Next (#493244) →

C₄×#2179 #493243

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

Aliases

Subgroups

724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400439);