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C₅×#829 #91072

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 148);