Finite Group Databasebeta

?

← Prev (#521238) Next (#521240) →

C₄×#2768 #521239

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

Aliases

Subgroups

2466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

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, 428435);