Finite Group Databasebeta

?

← Prev (#483316) Next (#483318) →

C₂×#11997 #483317

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

Aliases

Subgroups

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390513);