Finite Group Databasebeta

?

← Prev (#87277) Next (#87279) →

C₂×#5836 #87278

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(3,4,5)(6,10,11,8)(7,14,16,21)(9,18,19,17)(12,13,20,15);(1,2)(6,9,11,19)(7,13,16,15)(8,17,10,18)(12,14,20,21);(6,8,11,10)(7,12,16,20)(9,18,19,17)(13,21,15,14);(4,5)(6,7)(8,12)(9,13)(10,20)(11,16)(14,17)(15,19)(18,21);(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, 19854);