Finite Group Databasebeta

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C₂×#151060 #72321170

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

Aliases

Subgroups

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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