Finite Group Databasebeta

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C₉×#3288 #11768009

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

696 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

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

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2020);