Finite Group Databasebeta

?

← Prev (#86084) Next (#86086) →

C₂×#5690 #86085

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18661);