Finite Group Databasebeta

?

← Prev (#10632006) Next (#10632008) →

C₃×#13400 #10632007

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 35 points:

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

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, 6388);