Finite Group Databasebeta

?

← Prev (#359175) Next (#359177) →

C₄×#2032 #359176

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

Aliases

Subgroups

1501 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

(1,2,3,4);(5,6)(7,10)(8,15,17,11)(9,12)(13,20,16,18)(14,19);(5,7)(6,10)(8,16,17,13)(9,14)(11,18,15,20)(12,19);(5,8)(6,11)(7,13)(9,17)(10,18)(12,15)(14,16)(19,20)

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, 266372);