Finite Group Databasebeta

?

← Prev (#16817269) Next (#16817271) →

C₂₉×#3556 #16817270

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 61 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2288);