Finite Group Databasebeta

?

← Prev (#7622925) Next (#7622927) →

C₂×#33584 #7622926

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

Aliases

Subgroups

2150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 7530122);