Finite Group Databasebeta

?

← Prev (#10652158) Next (#10652160) →

C₃×#33552 #10652159

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3)(4,5)(6,14)(7,11)(8,12)(9,13)(10,17)(15,27)(16,28)(18,24)(19,25)(20,33)(21,26)(22,30)(23,31)(29,35)(32,34);(4,6)(5,10)(7,15)(8,17)(9,16)(11,22)(12,14)(13,23)(18,30)(19,29)(20,32)(21,31)(24,27)(25,34)(26,28)(33,35);(4,7,9,19)(5,11,13,25)(6,15,16,29)(8,20,21,18)(10,22,23,34)(12,24,26,33)(14,27,28,35)(17,32,31,30);(6,16)(10,23)(14,28)(15,29)(17,31)(22,34)(27,35)(30,32)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 26540);