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D₃×#400 #78340

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3)(5,7)(9,13)(12,15)(16,18,19,23)(17,21,20,22);(4,5)(6,7)(8,10,11,14)(9,12,13,15)(17,20)(18,23);(8,9)(10,12)(11,13)(14,15)(16,17,19,20)(18,22,23,21);(2,3)

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, 10916);