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C₃×Q₈×D₉ #88717

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 364);