Finite Group Databasebeta

?

← Prev (#86114) Next (#86116) →

C₂×#5708 #86115

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1124 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)(7,10)(9,12)(11,13)(14,16,17,21)(15,19,18,20);(6,7,9,11)(8,10,12,13)(15,18)(19,20);(8,12)(10,13)(14,15,17,18)(16,20,21,19);(4,5)(8,12)(10,13);(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, 18691);