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C₂×C₄×#237 #85748

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18324);