Finite Group Databasebeta

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C₉×#3018 #11767739

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1086 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)(10,11)(12,19)(13,17)(14,22)(15,18)(16,20)(21,24)(23,25);(10,12)(11,16)(13,20)(14,23)(15,21)(17,24)(18,25)(19,22);(10,11)(12,16)(13,17)(14,22)(15,18)(19,23)(20,24)(21,25);(10,13,15,14)(11,17,18,22)(12,20,21,23)(16,24,25,19)

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 1750);