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D₃×D₃₂ #69375

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 1951);