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C₂×D₃×#137 #87193

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

Aliases

Splittings

Subgroups

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

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, 19769);