Finite Group Databasebeta

?

← Prev (#483319) Next (#483321) →

C₂×#11999 #483320

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

Aliases

Subgroups

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4,5,7,6,8,9,10)(11,12)(13,22,25,36)(14,19)(15,28)(16,31)(17,21)(18,24,33,38)(20,29)(23,35,26,40)(27,34)(30,41)(32,37,42,39);(11,13,15,24,16,26,29,39,17,25,30,38,14,23,27,37)(12,18,20,22,19,32,28,35,21,33,34,36,31,42,41,40);(11,14,17,16)(12,19,21,31)(13,23,25,26)(15,27,30,29)(18,32,33,42)(20,28,34,41)(22,35,36,40)(24,37,38,39)

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, 390516);