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C₅×#4493 #11746192

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,11,12,20,14,23,25,22)(10,15,16,28,18,30,32,29)(13,26,24,21,27,37,39,38)(17,33,31,19,34,35,40,36);(7,8)(9,10,13,17,25,32,39,40,14,18,27,34,12,16,24,31)(11,19,21,28,20,35,37,30,23,36,38,29,22,33,26,15)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 387);