Finite Group Databasebeta

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C₉×#1438 #11766159

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 25 points:

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

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 170);