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D₃×#564 #87142

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

Aliases

Splittings

Subgroups

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 19718);