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C₂×D₃×#135 #87182

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19758);