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D₃×#578 #87209

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

Aliases

Splittings

Subgroups

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19785);