Finite Group Databasebeta

?

← Prev (#499048) Next (#499050) →

C₂×#13397 #499049

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

Aliases

Subgroups

1050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4,10,16)(5,11,20,36)(6,21,23,55)(7,27,31,43)(8,15,9,14)(12,37,39,24)(13,29,44,30)(17,46,47,66)(18,49,52,65)(19,45,32,35)(22,57,53,54)(25,56,26,42)(28,41,59,40)(33,61,62,48)(34,60,63,51)(38,58,64,50);(3,5)(4,11)(6,22)(7,18)(8,32)(9,19)(10,20)(12,38)(13,34)(14,45)(15,35)(16,36)(17,25)(21,54)(23,53)(24,58)(26,47)(27,49)(28,48)(29,60)(30,51)(31,52)(33,40)(37,50)(39,64)(41,62)(42,46)(43,65)(44,63)(55,57)(56,66)(59,61);(3,6,9,25,10,23,8,26)(4,12,15,40,16,39,14,41)(5,17,19,53,20,47,32,22)(7,28,30,37,31,59,29,24)(11,33,35,64,36,62,45,38)(13,42,27,55,44,56,43,21)(18,50,51,61,52,58,60,48)(34,57,49,66,63,54,65,46)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406245);