Finite Group Databasebeta

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D₃×#12780 #72247790

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

4838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

102 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((34,35), (1,3,7,17)(2,9)(4,14,6,16)(5,19,20,15)(8,22)(10,28)(11,13)(12,26)(18,31,21,30)(23,32)(24,25)(27,29)(33,34,35), (1,2,4,10)(3,13,14,9)(5,8,18,23)(6,11,7,12)(15,29,30,22)(16,26,17,28)(19,32,31,25)(20,24,21,27), (2,8,12,24)(4,6)(9,25,26,22)(10,27,11,23)(13,29,28,32)(14,16)(18,21)(30,31));