Finite Group Databasebeta

?

← Prev (#85738) Next (#85740) →

C₂×#5527 #85739

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1328 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)(14,17,18,21)(15,19,16,20);(7,10)(11,13)(14,16,18,15)(17,20,21,19);(6,7)(8,11)(9,10)(12,13)(14,15)(16,18)(17,19)(20,21);(4,5)(17,21)(19,20);(1,2)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18315);