Finite Group Databasebeta

?

← Prev (#493102) Next (#493104) →

C₂×#12657 #493103

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

Aliases

Subgroups

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

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, 400299);