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C₂×D₃×C₂²⋊Q₈ #85974

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 17 points:

(3,4,5)(6,7)(8,9)(10,11)(12,14)(13,15)(16,17);(1,2)(10,12,13,17)(11,14,15,16);(7,9)(10,11,13,15)(12,16,17,14);(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, 18550);