Finite Group Databasebeta

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C₂³×#67 #5970

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 13 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1529);