Finite Group Databasebeta

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C₅×#912 #91715

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 791);