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C₅×#5769 #11756154

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

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, 10349);