Finite Group Databasebeta

?

← Prev (#63502) Next (#63504) →

C₂×#3674 #63503

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 27 points:

(3,4,7,9,11,10,5,8,6)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(4,6)(5,9)(7,8)(10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21);(1,2)

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 151);