Finite Group Databasebeta

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C₅×#870 #91673

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3)(5,9)(8,11)(12,14,15,18)(13,17,16,19)(20,21,22,23,24);(4,6,7,10)(5,8,9,11)(13,16)(17,19);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13,15,16)(14,17,18,19)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 749);