Finite Group Databasebeta

?

← Prev (#72258450) Next (#72258452) →

D₃×#33469 #72258451

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

3832 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 35 points:

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

Conjugacy classes & character table

138 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((1,2), (5,12)(6,15)(11,27)(13,29)(16,18)(17,32)(22,34)(28,30), (5,11,12,27)(7,19)(8,21)(10,23,24,25)(13,30,29,28)(14,31,26,33)(16,22)(17,32)(18,34)(20,35), (2,3)(4,6)(5,10,12,24)(7,18)(8,17)(9,15)(11,23,27,25)(13,26,29,14)(16,20)(19,34)(21,32)(22,35)(28,31,30,33), (4,5,7,11,8,13,19,28,9,12,20,27,21,29,35,30)(6,14,16,31,17,10,22,25,15,26,18,33,32,24,34,23));