Finite Group Databasebeta

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C₅×#5648 #11756033

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2,3,4,5)(6,7,8)(10,12)(13,16,17,24)(14,19,20,23)(15,22,21,27)(18,26,25,28);(9,10)(11,12)(15,21)(18,25)(22,27)(26,28);(13,15)(14,18)(16,22)(17,21)(19,26)(20,25)(23,28)(24,27);(7,8)(13,14,17,20)(15,18,21,25)(16,23,24,19)(22,28,27,26)

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, 10228);