Finite Group Databasebeta

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C₅×#5546 #11755931

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10126);