Finite Group Databasebeta

?

← Prev (#494330) Next (#494332) →

C₂×#12954 #494331

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

Aliases

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401527);