Finite Group Databasebeta

?

← Prev (#87558) Next (#87560) →

C₂³×#239 #87559

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 17 points:

(1,2)(3,4)(5,6)(7,8,9)(10,12,13,16)(11,14,15,17);(10,11,13,15)(12,17,16,14);(8,9)(12,16)(14,17);(5,6);(3,4);(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, 20135);